UC-NRLF 


B    M    D73    7Si 

FREEZING-POINT 
BOILING-POINT 

AND  CONDUCTIVITY  METHODS 

JONES 


MEMCAL    tSCMOOL 
LUISmAllSY 


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in  2007  witin  funding  from 

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THE  FREEZINC-POINT,  BOILING-POINT 
AND  CONDUCTIVITY  METHODS. 


...™™..,,.^«^™ 

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THE 


Freezing-Point,  Boiling-Point 


AND 


Conductivity  Methods 


Second  Edition,  Completely  Revised 


BY 
HARRY    C.  JONES 

Professor  of   Physical  Chemistry  in  The  Johns  Hopkins  University 


EASTON.  PA. 

THE  CHEMICAL  PUBLISHING  CO. 

1912 

{All  rightt^reserved) 


Copyright,   1912,  by  Edward  Hart 


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PREFACE 


I  have  been  impressed,  in  teaching  the  physical  chem- 
ical methods  in  the  laboratory,  with  the  fact  that  there 
is  no  readily  accessible  place  in  which  they  are  treated 
satisfactorily  from  both  the  standpoint  of  theory  and  of 
practice.  In  the  text-books,  the  theoretical  side  is  de- 
veloped, and  usually  without  sufficient  attention  to  the 
details  of  manipulation  to  enable  them  to  be  applied 
successfully  in  the  laboratory.  In  the  laboratory  man- 
uals, on  the  other  hand,  these  methods  are  often  treated 
largely  from  the  mechanical  side,  and  their  theoretical 
bearing  thus  lost  sight  of. 

The  physical  chemical  methods,  which  find  most  fre- 
quent application  in  the  laboratory,  are  probably  those 
based  upon  the  lowering  of  the  freezing-point  and  the 
rise  in  the  boiling-point  of  a  solvent  produced  by  a  dis- 
solved substance,  and  the  electrolytic  conductivity  of 
solutions  of  electrolytes.  It  is  my  chief  object  in 
preparing  this  little  work  to  give  an  account  of  the 
operations  involved  in  carrying  out  these  methods  in 
the  laboratory.  But  since  the  mere  mechanical  applica- 
tion of  any  scientific  method  is  a  matter  of  comparatively 
little  significance,  I  have  aimed  to  give,  also,  enough  of 
the  theoretical  ground  on  which  each  of  them  rests,  to 
enable  the  student  to  work  with  them  intelligently,  and 
to  see  clearly  their  scientific  significance  and  use. 

Harry  C.  Jones. 


PREFACE  TO  SECOND  EDITION 


The  demand  for  a  second  edition  shows  that  this  little 
laboratory  manual,  which  was  first  published  in  the  very 
early  days  of  Physical  Chemistry  in  America,  has  met 
a  want. 

The  methods  herein  discussed  are  those  most  frequently 
used  in  the  physical  chemical  laboratory.  In  revising  this 
booklet  for  a  second  edition  the  aim  has  been  to  bring  it 
up  to  date.  A  number  of  minor  corrections  have  been 
introduced,  larger  tables  of  freezing-point  and  boiling- 
point  constants  have  been  inserted,  and  the  boiling-point 
method  applied  to  the  measurement  of  electrolytic  dis- 
sociation in  nonaqueous  solvents. 

The  conductivity  method  has  been  described  more  near- 
ly as  carried  out  to-day  and,  it  is  hoped,  with  sufficient 
detail  to  enable  the  method  to  be  used  successfully  in  the 
laboratory. 

The  drawings  for  figures  lo  and  12  have  been  made  by 
my  assistant.  Dr.  E.  P.  Wightman. 

H.  C.  J. 


CONTENTS 


PART  I 
THE  FREEZING-POINT  METHOD 

PA&B 

Theoretical  Discussion i 

Early  History i 

Work  of  Raoult i,  2 

Molecular  Lowering  for  Different  Solvents 3 

Molecular  Lowering  in  Aqueous  Solutions 4 

Theory  of  Electrolytic  Dissociation 5 

Calculation  of  the  Molecular  Lowering 6,  7 

Experimental  Verification 8 

Calculation  of  Molecular  Weights  from  Lowering  of  Freezing- 
Point    8,  9 

The  Application  of  the  Freezing-Point  Method  to  the  Determina- 
tion of  Molecular  Weights  in  Solution 10 

The  Apparatus  of  Beckmann 10-13 

Carrying  out  a  Determination   13-15 

Correction  for  the  Separation  of  Ice 15,  16 

The  Application  of  the  Freezing-Point  Method  to  the  Measure- 
ment of  Electrolytic  Dissociation 16 

The  Method  of  Calculating  Dissociation  from  Lowering  of 

Freezing-Point 16,  17 

The  Method  of  Work 18 

The  Apparatus  of  Jones 19-22 

Comparison  of  the  Results  with  the  Dissociation  from  Con- 
ductivity Measurements 23 


VI  CONTENTS 

PART  II 

THE  BOILING-POINT  METHOD 

PAGE 

Theoretical  Discussion 25 

Historical 25,  26 

Work  of  Raoult 26,  27 

The  Relative  Lowering  of  the  Vapor-Tension 28 

Calculation  of  Molecular  Weights  from  Lowering  of  the  Va- 
por-Tension        29 

Beckmann's  Work  on  Rise  in  Boiling-Point 29,  30 

Calculation  of  Molecular  Weights  from  Rise  in  the  Boiling- 
Point  of  Solvents 30 

Values  of  the  Constants  for  Solvents 31 

Relations  between  Boiling-Point  and  Freezing-Point   Meth- 
ods   31,  32 

The  Application  of  the  Boiling-Point  Method  to  the  Determina- 
tion of  Molecular  Weights  in  Solution 32 

The  Apparatus  of  Beckmann 33-35 

The  Apparatus  of  Hite 35-37 

The  Apparatus  of  Jones 36-39 

Carrying  Out  a  Determination  3942 

Correction  for  Separation  of  Vapor 42 

Results  of  Measurements 43,  44 

RESULTS  FOR  A  FEW  SUBSTANCES 

The  Application  of  the  Boiling-Point  Method  to  the  Measure- 
ment of  Electrolytic  Dissociation   44 

Measurements  of  Electrolytic  Dissociation 45,  46 

Calculation  of  the  Dissociation 46-48 

PART  III 

THE  CONDUCTIVITY  METHOD 

Two  Classes  of  Conductors 49 

Electrolytes  and  Non-Electrolytes 49 

Specific  Conductivity 50,  51 

Molecular  Conductivity 51 

Dissociation  Measured  by  Conductivity  Method 52,  53 

Determination  of  /*„ 53-57 


CONTENTS  Vll 


PAGB 

The  Application  of  the  Conductivity  Method  to  the  Measurement 

of  Electrolytic  Dissociation 57 

The  Apparatus  Employed 57-59 

Calculation  of  the  Molecular  Conductivity 59,  60 

Wheatstone  Bridge 61 

Temperature  Coefficient  of  Conductivity 62 

Thermoregulator    63 

Calibrating  the  Wire 65-67 

Carrying  Out  a  Conductivity  Measurement 67 

Determination  of  the  Cell  Constant 68 

Precautions 69 

Correction  for  the  Conductivity  of  Water 70,  71 

The  Purification  of  Water 71-73 

Substances  to  be  Used 73 

Results  for  a  Few  Substances 73-75 


PART  I 


THE  FREEZING-POINT  METHOD 


THEORETICAL 

It  has  long  been  known  that  when  a  solid  is  dissolved 
in  a  liquid,  the  freezing-point  of  the  solution  is  lower 
than  that  of  the  solvent.  The  first  quantitative  relation 
we  owe  to  Blagden,  who  pointed  out  that  the  lowering 
of  the  freezing-point  of  water,  produced  by  different 
amounts  of  the  same  substance,  was  proportional  to 
the  amount  of  substance  present.  This  same  fact  was 
rediscovered  much  later  by  Riidorff.^  A  marked  ad- 
vance was  made  by  Coppet,^  who  dealt  with  comparable, 
rather  than  with  equal  amounts  of  different  substances. 
He  used  quantities  of  different  substances  which  bore  to 
one  another  the  same  relation  as  their  molecular  weights, 
and  found  that  such  quantities  of  substances  which  are 
chemically  allied,  produce  very  nearly  the  same  lower- 
ing of  the  freezing-point  of  any  given  solvent.  In  a 
word,  the  lowering  of  the  freezing-point  of  a  solvent  by 
a  dissolved  substance,  is  proportional  to  the  number  of 
parts  of  the  substance  present. 

This  is  about  what  was  known  when  the  problem  was 
taken  up  by  Raoult,  and  it  is  to  him  more  than  to  anyone 
else  that  we  owe  the  present  development  of  the  freez- 
ing-point method.  He  investigated  aqueous  solutions  of 
organic  compounds,  and  found  that  the  lowering  pro- 
duced by  molecular  quantities  was  very  nearly  a  con- 

1  Phil.  Trans.,  78,  277. 

2  Pogg.  Ann.,  114,  63  (1861),  145,  599  (1872). 
8  Ann.  Chim.  Phys.,  [4],  33,  366  (1871). 


2  THE  FREEZING-POINT    METHOD 

stant.  He  used  other  solvents,  such  as  benzene,  and 
found  that  comparable  quantities  of  dissolved  substances 
produced  the  same  lowering  of  its  freezing-point.  His 
investigations  included  nitrobenzene,  ethylene  bromide, 
formic  and  acetic  acids,  and  in  each  solvent  a  large 
number  of  substances  was  dissolved.  He  was  thus  in 
a  position  not  only  to  compare  the  lowerings  produced 
by  different  substances  in  the  same  solvent,  but  the  low- 
erings in  different  solvents. 

As  the  result  of  this  work,  Raoult  announced  the  fol- 
lowing generalization. 

One  molecule  of  any  complex  substance  dissolved  in 
one  hundred  molecules  of  a  liquid,  lowers  the  freezing- 
point  of  the  liquid  by  nearly  a  constant  amount,  which 
is  0.62°.    This  has  been  shown  not  to  hold  rigidly. 

When  a  gram-molecular  weight  of  any  substance  is 
dissolved  in  say  100  grams  of  a  solvent,  the  lowering  of 
the  freezing-point  of  the  solvent  is  a  constant,  regardless 
of  the  nature  of  the  substance,  provided  that  there  is 
no  aggregation  of  the  molecules  of  the  substance,  and 
no  dissociation.  This  was  shown  by  Raoult^  to  hold  ap- 
proximately for  a  large  number  of  substances,  and  for 
several  solvents.  The  molecular  lowering,  which  is  the 
lowering  produced  by  a  gram-molecular  weight  of  the 
substance  in  100  grams  of  the  solvent,  was  calculated  by 
him  thus : 

If  g  grams  of  the  substance  are  dissolved  in  100  grams 
of  the  solvent,  if  w  is  the  molecular  weight  of  the  sub- 
stance, and  A  the  lowering  of  the  freezing-point  of  the 
solvent  produced  by  the  presence  of  g  grams  of  the  sub- 

1  Ann.  Chim.  Phys.,  [6],  3,  66  (1884). 


THE   FREEZING-POINT    METHOD  3 

stance,  then  the  molecular  lowering  is  calculated  from 
the  formula: 

,  Molecular  lowering  = . 

g 

A  few  results  will  show  the  values  of  the  molecular 

lowering  for  different  solvents. 

SoiyVENT,  AcKTic  Acid. 

Molecular 
IrfOwering. 

Methyl  iodide 38.8 

Aldehyde    38,4 

Acetone 38.  i 

Benzoic  acid 43.0 

Ethyl  alcohol 36.4 

Acetamide 36.  i 

Stannic  chloride 41.3 

Carbon  disulphide 35.6 

Sulphuric  acid 18.6 

Hydrochloric  acid 17.2 

SoivVENT,  Benzene. 

Methyl  iodide 50.4 

Anthracene    51.2 

Ether 49.7 

Acetone 49. 3 

Chloral    50.3 

Stannic  chloride 48.8 

Methyl  alcohol 25.3 

Ethyl  alcohol 28.2 

Benzoic  acid 25.4 

S01.VENT,  Water. 

Methyl  alcohol 17.3 

Cane-sugar 18.5 

Acetamide 17.8 

Chloral  hydrate 18.9 

Milk-sugar 18.  r 

Acetone 1 7.  i 

Hydrochloric  acid 39.  i 

Nitric  acid 35.8 

Sulphuric  acid 38. 2 

Sodium  hydroxide 36. 2 

Potassium  chloride 33.6 


4  THE   FREEZING-POINT    METHOD 

A  careful  study  of  these  results  will  bring  out  some 
interesting  facts.  The  value  of  the  molecular  lowering 
of  acetic  acid  and  of  benzene  is  very  nearly  a  constant 
for  each  solvent.  This  is  true  for  a  large  number  of 
substances  of  the  general  type  of  most  of  those  given 
above,  i.  e.,  non-electrolytes.  There  are,  however,  ex- 
ceptions for  these  solvents.  In  the  case  of  acetic  acid, 
there  are  a  few  substances  known  which,  like  sulphuric 
acid,  give  a  molecular  lowering  of  only  one-half  that 
produced  by  the  non-electrolytes.  In  benzene  there  are 
also  a  few  exceptions,  but  in  this  case  the  substances 
which  give  only  half  the  normal  molecular  lowering,  are 
either  non-electrolytes  like  the  alcohols,  or  weakly  dis- 
sociated acids  like  acetic,  benzoic,  etc.  The  probable  sig- 
nificance of  the  small  molecular  lowering  produced  by 
some  substances  is,  that  they  are  in  a  state  of  molecular 
association  in  the  particular  solvent.  When  the  molecu- 
lar lowering,  in  the  case  of  two  undissociated  com- 
pounds dissolved  in  a  given  solvent,  is  twice  as  great 
for  one  as  for  the  other,  it  means  that  twice  as  many 
molecules  of  the  second  are  aggregated  into  a  unit  as  of 
the  first.  If  the  molecules  of  the  one  exist  singly  in  solu- 
tion, those  of  the  second  are  combined  in  twos.  This  will 
be  seen  at  once,  if  we  remember  that  the  lowering  of  the 
freezing-point  of  a  solvent  depends  only  on  the  relative 
number  of  parts  of  the  solvent  and  of  the  dissolved  sub- 
stance. 

When  we  come  to  the  results  with  water  as  a  solvent 
we  have  to  deal  with  an  entirely  new  set  of  phenomena. 
The  results  given  above  are  a  •  few  taken  from  a  large 
number.  Compounds  like  the  non-electrolytes,  give  a 
molecular  lowering   for   water  which   is   very   nearly   a 


THE   FREEZING-POINT    METHOD  5 

constant,  and  which  is  approximately  18.6.  This  is  true 
for  such  a  large  number^  of  substances  that  have  been 
investigated,  that  there  is  no  reason  for  regarding  them 
as  being  exceptions.  On  the  other  hand,  all  the  strong 
electrolytes,  including  the  strong  acids,  strong  bases, 
and  salts  of  strong  acids  with  strong  bases,  weak 
acids  with  strong  bases,  and  weak  bases  with  strong 
acids,  give  molecular  lowerings  which  are  greater  than 
the  value  18.6.  The  explanation  that  has  been  offered 
by  Arrhenius,^  to  account  for  this  and  related  facts  is 
that  the  molecules  of  the  electrolytes  do  not  exist  as 
such  in  aqueous  solution.  They  are  dissociated  into  parts 
called  ions,  and  the  amount  of  such  dissociation  depends, 
for  a  given  substance,  chiefly  on  the  dilution  of  the  solu- 
tion. In  a  very  dilute  solution  of  a  strongly  dissociated 
electrolyte,  we  have  practically  no  molecules  present,  only 
ions.  If  the  molecule  is  binary,  each  yields  two  ions,  and 
since  an  ion  lowers  the  freezing-point  of  the  solvent  as 
much  as  a  molecule,  the  molecular  lowering  for  such  sub- 
stances, at  high  dilution,  is  twice  as  great  as  where  there 
is  no  dissociation.  If  the  molecule  dissociates  into  three 
ions,  and  the  dilution  is  such  that  the  dissociation  is  com- 
plete, the  lowering  of  the  freezing-point  will  be  three 
times  as  great  as  where  there  is  no  dissociation,  as  is  the 
case  with  the  non-electrolytes. 

It  is  stated  above  that  in  aqueous  solutions  the  mole- 
cules break  down  into  parts  called  ions.  It  is  so  easy 
to  confuse  ions  with  atoms,  and  this  is  so  frequently 
done,  that  a  word  of  caution  here  is  not  out  of  place. 
An  ion  is  not  an  atom,  but  is  an  atom  or  group  of  atoms 
charged  with  electricity.     The  resemblance  between  the 

1  Ann,  Chim.  Phys.  [5],  28,  137  (1883). 

2  Ztschr.  phys.  Chem,,  i,  631  (1887). 

2 


6  the;   i^REJDZING-POINT    METHOD 

two  is  far  less  close  than  might  be  imagined.  The  prop- 
erties of  many  of  the  atoms  with  the  exception  of  their 
mass,  could  not  be  foretold  from  the  corresponding  prop- 
erties of  the  ions,  with  any  degree  of  probability.  An 
atom  of  potassium  has  properties  so  different  from  an 
ion  of  potassium,  that  one  is  more  impressed  by  their  dif- 
ference than  by  their  resemblance. 

In  some  cases,  as  with  the  non-electrolytes,  we  have 
then  to  deal  only  with  molecules  in  solution  in  water, 
while  with  the  electrolytes  we  have  both  molecules  and 
ions,  or  only  ions,  depending  on  the  dilution  of  the  solu- 
tion. 

That  the  true  value  of  the  molecular  lowering  for 
water,  when  there  is  neither  molecular  aggregation  nor 
electrolytic  dissociation,  is  18.6,  has  been  shown  theo- 
retically by  van't  Hoff,^  and  more  clearly  presented  by 
Oswald,^  thus : 

Given  a  solution  that  contains  n  gram-molecules  of 
the  dissolved  substance  in  N  gram-molecules  of  the  sol- 
vent. Let  T  be  the  temperature  of  solidification  of  the 
solvent  and  A  the  lowering  of  its  freezing-point  produced 
by  the  dissolved  substance.  Let  enough  of  the  solvent 
solidify    to    dissolve    a    molecule    of    the    substance, 

JV 


(— 

\  n 


molecules  ) .  Let  A.  be  the  molecular  heat  of  fusion 
n  / 

of  one  gram  of  the  solvent,  the  amount  of  heat  set  free 
in  the  above  process  =  — A.    If  the  ice  is  now  separated 

from  the  solution,  warmed  to  the  temperature  T, 
fused,  and  finally  allowed  to  mix  with  the  solution  which 
has  also  been  warmed  to  the  same  temperature,  by  pass- 

1  Ztschr.  phys.  Chem.,  i,  481  (1887). 

2  I^ehrbuch  allg.  Chem.,  i,  760. 


THE   FREEZING-POINT    METHOD  / 

ing  through  a  semi-permeable  membrane,    an    osmotic 

pressure  p  will  be  exerted.     If  the  volume  of  the  solvent 

N 
which  solidifies  is  v,  the  work  equals /z',  the  heat  — X, 

It 

pvn  A* 

But  pv  =  RT  and  R  =  2  cal.  Substituting  we  have: 

Let  M  be  the  molecular  weight  of  the  solvent,  and 
placing  JV  =  —rry  we  have: 

A  =  .--— (i) 

100       A  ^ 

C 
In  the  Raoult  formula  w  =  — j  ,    »«   is  the  molecular 

A 

weight  of  the  dissolved  substance,  A  is  the  specific  low- 
ering of  the  freezing-point,  which  equals  — ,  in  which/ 

is  the  percentage  composition  of  the  solution,  and  C  is 
a  constant,  w,  the  number  of  molecules  of  the  dis- 
solved substance  in  100  grams  of  the  solvent  =  ~  . 

tft 

A=:C« (2) 

From  (i)  and  (2)  we  have  : 

C=—    — 

100  *     \ 

If  L  is  the  heat  of  fusion  of  one  gram  of  the  solvent, 
A  =:  LM,  and 

*  Work  done  is  to  the  heat  set  free  as  the  difference  in  temperature  is  to  the 

absolute  temperature  ;    pv  :  —X  :  :  A  :  T. 
n 


THE^   FREEZING-POINT    METHOD 
2  7' 


C  = 


looZ^* 

The  absolute  temperature  T  of  the  freezing-point  of 
water  is  273°,  and  L,  the  heat  of  fusion  of  one  gram  of 
water,  was  taken  by  van't  Hoff  as  79*^.^  When  th.ese 
values  are  inserted  in  the  above  expression,  C  =  18.9. 
The  value  of  L  is  probably  more  nearly  79.7  when 
C  becomes  18.8. 

I  have  shown  experimentally^  that  the  value  of  C  for 

water,  as  determined  with  solutions  of  urea,  ethyl  and 

propyl  alcohols,  is  respectively: 

18.18 
18.76 

18.77' 

The  formula  of  van't  Hoff  applies  to  the  calculation 
of  the  freezing-point  constant  of  any  solvent. 

The  freezing-point  method  has  thus  two  distinct  ap- 
plications :  To  determine  the  molecular  weight  in  solu- 
tion of  compounds  which  are  not  dissociated  by  the 
solvent;  and  to  measure  the  amount  of  the  dissociation 
of  electrolytes  in  solutions  of  different  concentrations. 

The  applicability  of  the  freezing-point  method  to  the 
determination  of  the  molecular  weights  of  substances  in 
solution,  was  pointed  out  by  Raoult.*  If  we  represent 
the  unknown  molecular  weight  of  a  substance  by  m,  the 
molecular  lowering  or  constant  of  the  solvent  by  C,  and 
the  lowering  of  the  freezing-point  produced  by  a  one 
per  cent,  solution  of  the  dissolved  substance  by  S,  we  have 

C 

1  Ztschr.  phys.  Chem.  i,  497  (1887). 
s  Ibid,  la,  653  (1885). 

»  The  most  recent  work  indicates  that  the  freezing-point  constant  for  water 
is  1.86. 

*Compt.  Rend.,  loi,  1056  (1885). 


the;  freezing-point  method  9 

If  the  weight  of  the  solvent  used  is  W,  that  of  the  dis- 
solved substance  w,  and  the  observed  lowering  of  the 
freezing-point  A, 

lOOW  ' 

Substituting  this  value  of  5*  in  the  above  expression,  we 
have 

loo  Cw 

If  the  constant  C  is  multiplied  by  loo  and  termed  C 
the  expression  becomes 

Cw 

The  values  of  C  for  a  number  of  the  solvents  common- 
ly used  with  the  freezing-point  method  are 

Melting-point  Constant 

Acetic  Acid 17.0  39.0 

Acetoxime 59.4  56.0 

Aniline —5-96  58.7 

Benzene 4.97  49.0 

Benzoic  Acid 123,0  78.5 

Bromoform 8.0  144.0 

Dimethylaniline 1.96  58.0 

Dinitrobenzene  (w)  91.0  106.0 

Diphenylmethane 26.3  67.0 

Triphenyl  methane 93.0  124.5 

Ethylenebromide 8.0  118. o 

Formic  Acid 8.0  28.0 

Naphthalene 80.  i  68.0 

Nitrobenzene 5.3  70.5 

Phenanthrene 96.25  120.0 

Phenol 38.5  74.0 

Phosphorus 44.0  390.0 

Resorcine i  lo.o  65.0 

Thymol 48.2  80.0 

Water 0.0  18.6 


10 


TH^  IfREEZING-POiNT    METHOD 


The  Application  of  the  Freezing-Point  Method  to  the 
Determination  of  Molecular  Weights  in  Solution 

Beckmann^  has  devised  a  form  of  apparatus  that  is 
both  simple  and  efficient.     C   (Fig.  i)   is  a  small  glass 


Fig.  I. 

battery- jar  covered  with  some  poorly  conductirig  sub- 
stance, and  which  is  filled  with  the  freezing  material. 
A  mixture  of  finely  powdered  ice  and  salt  is  convenient, 
care  being  taken  to  use  the  smallest  amount  of  salt  that 

1  Ztschr,  phys.  Chem.,  3,  638  (1888), 


the;  Freezing-point  method  ii 

will  freeze  the  solution.  B  is  a  thick-walled  glass  tube, 
into  which  tube  A,  containing  the  solution,  is  inserted.  A 
side  tube  attached  to  tube  A,  is  thought  to  be  useful  in 
introducing  the  substance  whose  molecular  weight  is  to 
be  ascertained,  but  can  be  readily  dispensed  with.  The 
thermometer,  of  the  Beckmann  differential  type,  is  fitted 
into  the  tube  A,  by  means  of  a  cork,  which  can  be  easily 
removed.  The  stirrer  S  passes  through  the  same  cork, 
and  must  be  of  such  form  and  dimensions  as  to  move 
freely  up  and  down  between  the  inner  walls  of  the  tube 
and  the  bulb  of  the  thermometer. 

A  small  glass  rod,  bent  at  the  bottom  in  the  form  of  a 
ring,  which  will  easily  enter  the  glass  tube  A,  is  quite 
efficient.  A  short  piece  of  glass  tubing,  through  which 
this  rod  will  move  freely,  is  forced  through  a  hole  in 
the  cork  at  the  top  of  tube  A,  and  serves  both  to  hold 
the  stirrer  in  place,  and  to  allow  smoother  movement 
through  the  cork.  The  apparatus  of  the  following  di- 
mensions has  been  found  in  this  laboratory  to  be  con- 
venient. 

Tube  A  is  20  cm.  in  length  and  3  cm.  in  width.  B  is 
about  15  cm.  long  and  5,  cm.  wide.  The  glass  tube  used 
in  constructing  the  stirrer  should  be  about  2.5  mm.  in 
thickness.  A  thermometer  with  a  short,  thick  bulb,  such 
as  is  usually  furnished  on  the  market,  is  not  as  desirable 
as  one  with  a  bulb  that  is  longer  and  of  smaller  diam- 
eter; since  it  requires  a  longer  time  to  register  the  tem- 
perature of  the  liquid. 

In  case  the  solvent  used  is  hydroscopic,  some  precau- 
tion must  be  taken  to  protect  it  from  the  moisture  in  the 
air.  An  apparatus  satisfying  this  requirement  has 
been  constructed  also  by  Beckmann,^  by  forcing  the  air 

1  Ztschr.  phys.  Chem.,  7,  324  (1891). 


12  THE   FREEZING-POINT    METHOD 

which  enters  the  apparatus  to  pass  over  some  drying 
agent,  like  sulphuric  acid.  The  device  is  shown  in 
Fig.  2.  The  handle  of  the  stirrer  E  passes  through  a 
glass  tube,  into  which  the  side  tube  F,  containing  a  few 
drops  of  sulphuric  acid,  is  fused.  The  air  enters  through 
this  side  tube,  is  dried,  and  passes  out  through  the  tube 


Fig.  2. 

receiving  the  handle  of  the  stirrer.  The  remainder  of  the 
apparatus  is  of  exactly  the  same  form  as  that  shown  in 
Fig.  I,  except  that  it  is  provided  with  a  glass  siphon  H, 
for  removing  the  melted  freezing-mixture.  This  is  really 
superfluous,  since  a  piece  of  rubber  tubing  answers  the 
purpose  equally  well. 


TH^   ]?RKEZING-POINT    ME^THOD  I3 

Forms  of  apparatus  capable  of  yielding  far  more  accu- 
rate results  than  those  just  described,  have  been  devised 
and  used ;  ,but  since  such  extra  refinement  is  desirable 
rather  to  measure  dissociation  than  to  determine  molecu- 
lar weights,  reference  will  be  made  to  it  under  the  second 
application  of  the  freezing-point  method. 

Carrying  Out  a  Determination 

The  thermometer  must  first  be  so  adjusted  that  the 
freezing-point  of  water  falls  near  the  top  of  the  scale. 
To  accomplish  this,  water  is  poured  into  the  tube  A 
until  the  bulb  of  the  thermometer,  when  placed  in  posi- 
tion, is  covered.  Tube  A  is  placed  directly  in  the  freez- 
ing-mixture in  C,  and  the  water  allowed  to  freeze.  As 
soon  as  fine  particles  of  ice  separate,  tube  A  is  remov- 
ed from  the  freezing-mixture,  placed  in  tube  B,  and  the 
whole  then  introduced  again  into  the  freezing-mixture. 
The  thermometer  is  then  raised  out  of  the  water  contain- 
ing ice  particles,  allowed  to  remain  in  contact  with  the 
warmer  air  a  moment,  and  then  given  a  sudden  jar. 
The  mercury  falls  from  the  top  to  the  bottom  of  the 
upper  cup,  and  leaves  the  column  of  mercury  free  at  its 
upper  end.  The  thermometer  is  then  placed  again  in  the 
ice-cold  water,  and  if  the  end  of  the  mercury  column 
does  not  come  to  rest  on  the  upper  half  of  the  scale,  the 
process  just  described  is  repeated.  A  few  trials  generally 
suffice  to  bring  the  reading  on  the  thermometer  approxi- 
mately where  desired.- 

The  thermometer  being  adjusted,  tube  A  is  carefully 
dried,  closed  at  the  top  and  side  with  stoppers,  and 
weighed.  Enough  pure  water  is  poured  into  the  tube 
to  cover  the  bulb  of  the  thermometer  when  in  position, 
and  the  tube  is  again  weighed.     The  weight  of  the  sol- 


14  THE   FRDEZING-POINT    METHOD 

vent  employed  is  thus  determined.  The  stopper  is  then 
removed  from  the  top  of  the  tube  and  the  thermometer 
and  stirrer  placed  in  position.  Tube  A  is  inserted  into 
tube  B,  and  the  whole  system  into  the  freezing-mixture. 
During  the  cooling  of  the  solvent  the  stirrer  should  be 
raised  and  lowered  frequently.  The  water  will  cool 
down  below  its  freezing-temperature  often  a  degree  or 
more,  before  ice  will  begin  to  separate.  When  the  un- 
dercooling of  the  solvent  or  of  a  solution  is  very  much 
more  than  a  degree,  a  small  fragment  of  pure  ice  should 
be  thrown  into  the  undercooled  liquid.  This  will  start 
the  separation  of  ice,  which  will  continue  until  the  true 
freezing-temperature  is  reached. 

When  the  ice  begins  to  separate  the  mercury  column 
will  rise,  rapidly  at  first,  then  slower,  until  it  reaches 
the  point  of  equilibrium.  While  the  thermometer  is 
rising,  and  especially  when  near  the  point  of  rest,  it 
must  be  tapped  gently  to  prevent  the  mercury  from  lag- 
ging behind  in  the  capillary,  due  to  friction  against  its 
walls.  A  lead  pencil  is  convenient  to  use  in  jarring  the 
thermometer.  The  freezing-point  of  the  water  is  then 
noted  on  the  thermometer.  The  reading  on  the  ordi- 
nary Beckmann  instrument  can  easily  be  made  to  o.ooi° 
by  means  of  a  small  pocket  lens. 

The  tube  containing  the  solvent,  with  the  thermometer 
and  stirrer  in  position,  is  removed  from  the  freezing- 
mixture  and  the  ice  melted  by  seizing  the  tube  for  a 
few  moments  with  the  hand.  The  freezing-point  of  the 
water  is  then  redetermined  exactly  as  described  above. 
The  two  determinations  should  not  differ  more  than  two- 
or  three-thousandths  of  a  degree. 

The  substance  whose  molecular  weight  is  to  be  deter- 


TH^  :^rEe:zing-point  me^thod  15 

mined  is  weighed  in  a  weighing  tube,  poured  into  the 
solvent  and  brought  completely  into  solution.  If  cane- 
sugar  is  use,d,  that  quantity  is  taken  which  will  give  a 
solution  about  one-tenth  normal.  If  urea,  or  any  of  the 
alcohols  is  used,  a  more  concentrated  solution  may  be 
employed.  A  solution  of  cane-sugar,  dextrose,  etc.,  more 
concentrated  than  one-tenth  normal,  gives  abnormally 
large  depressions  of  the  freezing-point  of  water.  The 
reason  for  this  was  not  entirely  clear.  The  solution  is 
then  placed  in  the  freezing-mixture  and  its  freezing-point 
determined,  and  redetermined,  exactly  as  described  for 
the  solvent.  All  the  necessary  data  for  calculating  the 
molecular  weight  of  the  substance  from  the  expression 
already  given  are  thus  made  available. 

Correction  for  the  Separation  of  Ice 

A  certain  amount  of  the  solvent  separates  in  the  solid 
form  in  all  such  determinations,  and  the  solution  be- 
comes concentrated  by  just  this  amount.  The  freezing- 
point  of  the  solution,  as  read  on  the  thermometer,  is  there- 
fore always  lower  than  would  correspond  to  a  solution  of 
the  concentration  originally  used.  A  correction  for  the 
change  in  concentration,  due  to  the  separation  of  the 
solid  solvent,  must  be  introduced.  The  amount  of  the 
solvent  which  separates  in  the  solid  phase  can  easily  be 
determined,  knowing  the  amount  to  which  the  solution 
is  undercooled  before  the  ice  begins  to  separate,  the 
heat  of  fusion  of  a  unit  quantity  of  the  solvent,  and 
the  specific  heat  of  the  liquid.  The  fraction  of  the  sol- 
vent which  separates  is  calculated  thus,  as  was  pointed 
out  by  the  present  writer  :^ 

If  we  represent  by  u  the  amount  of  the  undercooling 

1  Ztschr.  phys.  Chem.,  12,  624  (1893). 


i6  the;  fre:i:zing-point  method 

of  the  solution  in  degrees  centigrade,  by  w  the  heat  of 
fusion  of  unit  weight  of  the  solvent,  by  s  the  specific  heat 
of  the  liquid,  and  by  T  the  fraction  that  will  solidify, 
we  have 

w 

When  water  is  used  as  a  solvent  ^  =  i  and  w  =  80. 
The  fraction  of  this  solvent  that  will  separate  as  a  solid, 
for  every  degree  of  undercooling,  is  therefore  ^/so,  ^^^ 
the  concentration  of  the  original  solution  is  increased  by 
just  so  much.  Instead  of  applying  the  correction  to  the 
concentration,  it  is  simpler  to  apply  it  directly  to  the 
freezing-point  lowering  itself. 

The  Application  of  the  Freezing-Point  Method  to  the 
Measurement  of  Electrolytic  Dissociation 

An  ion  lowers  the  freezing-point  of  a  given  quantity  of 
a  solvent  just  as  much  as  a  molecule.  If  a  molecule  dis- 
sociates into  two  ions  these  will  lower  the  freezing-point 
of  a  given  amount  of  a  solvent,  just  twice  as  much  as 
if  the  molecule  is  not  dissociated.  The  lowering  of  the 
freezing-point  of  a  given  solvent  by  a  partially  dissociated 
electrolyte,  depends  upon  the  relation  between  the  num- 
ber of  molecules  of  the  solvent,  and  the  sum  of  the 
molecules  plus  the  ions  of  the  dissolved  substance.  Thus, 
it  is  possible  at  any  given  dilution,  to  determine  the 
amount  to  which  an  electrolyte  is  dissociated.  The  cal- 
culation of  the  dissociation  from  the  freezing-point  low- 
ering is  simple.  The  molecular  lowering  of  the  freez- 
ing-point of  any  solvent  by  any  substance  was  defined  by 
Arrhenius^  as  the  lowering  produced  by  a  gram-molecu- 

1  Ztschr.  phys.  Chem.,  a,  494  (1888). 


THE  FREEZING-POINT    METHOD  1 7 

lar  weight  of  the  substance  in  a  liter  of  solution.  This 
can  be  taken  as  approximately  one-tenth  of  the  molecu- 
lar lowering  as  defined  by  Raoult.  For  our  present 
purpose  we  accept  the  definition  of  Arrhenius,  and  find 
that  the  molecular  lowering  of  the  freezing-point  of  wa- 
ter produced  by  a  gram-molecular  weight  of  a  non- 
electrolyte,  like  urea,  the  alcohols,  etc.,  in  a  liter  of  so- 
lution, is  the  constant  i.86°.  If  the  substance  used  is 
dissociated,  the  molecular  lowering  is  always  greater  than 
1.86°.  The  first  step  is  to  calculate  the  molecular  low- 
ering for  the  solution  in  question,  which  is  done  by  di- 
viding the  lowering  found  by  the  concentration  in  deci- 
mal part  of  normal.  If  there  were  only  molecules  pres- 
ent the  molecular  lowering  would  be  i.86°.  The  molecu- 
lar lowering  found  must  therefore  be  divided  by  i.86°, 
which  gives  the  value  of  the  van't  Hoff  coefficient  i,  for 
the  solution.^ 

Molecular  Lowering . 

1^86  "~  ^" 

If  the  molecule  breaks  down  into  two  ions,  the  percent- 
age dissociation^  a  (Arrhenius  activity  coefficient),  is 
expressed  thus 

a  ^  i  —  I . 

If  the  molecule  breaks  down  into  three  ions. 


t 
a  =  - 


If  into  n  ions, 


1  Ztschr,  phys.  Chem.,  i,  501  (iS 
*Ibtd,  11,535(1893). 


i8  the:  frdezing-point  method 

The  Method  of  Work 

Exactly  the  same  apparatus  may  be  used  as  was  em- 
ployed in  the  determination  of  molecular  weights.  The 
method  of  preparing  the  solutions  is,  however,  some- 
what different. 

The  solvent  is  poured  into  the  innermost  vessel  in 
quantity  large  enough  to  cover  the  bulb  of  the  thermom- 
eter, and  its  freezing-point  upon  the  thermometer  ascer- 
tained, as  in  a  molecular  weight  determination.  The 
solvent  is  then  completely  removed  from  the  vessel  and 
the  solution  of  known  concentration,  prepared  in  a  meas- 
uring flask,  introduced.  Its  freezing-point  is  then  de- 
termined exactly  as  previously  described,  including  the 
rapid  stirring,  the  tapping  of  the  thermometer,  the  intro- 
duction of  a  fragment  of  the  solid  solvent  when  neces- 
sary, and  the  correction  for  the  change  in  concentration 
due  to  the  separation  of  the  solid  solvent.  The  dilution 
of  the  solution  is  then  increased  one  and  a  half,  two, 
three,  four,  etc.,  times,  and  the  dissociation  determined 
for  each  dilution.  It  will  be  found  that  the  value  of  i, 
and  therefore  of  a,  always  increases  with  increase  in  dilu- 
tion. In  this  work  any  of  the  common  chlorides,  nitrates, 
bromides,  or  in  general  any  readily  soluble  electrolyte 
may  be  used. 

It  is  convenient  to  use  a  solution  of  pure  sodium  or 
potassium  chloride  of  concentration  about  0.5  normal, 
and  then  to  increase  the  dilution  of  this  solution  in 
several  steps,  as  indicated  above.  The  chlorides  and 
nitrates  break  down  into  two  ions  each,  the  sulphates 
into  three.  The  values  of  a  from  the  freezing-point 
method  should  be  preserved  and  compared  with  the  values 


THE   FREKZING-POINT    METHOD  I9 

of  a  for  the  same  solutions,  as  obtained  by  the  conduc- 
tivity method. 

Far  more  accurate  experimental  methods  have  been 
devised  and' used  for  measuring  the  freezing-point  lower- 
ings,  by  Loomis,^  Nernst  and  Abegg,^  Ponsot,*  myself,* 
and  others. 

A  form  of  apparatus,  which  was  found  by  the  writer 
to  give  excellent  results,  is  sketched  in  Fig.  3. 

A  is  a  large  metallic  vessel,  25  cm.  high  and  35  cm. 
wide.  This  is  surrounded  by  a  mantle  of  non-conducting 
material  to  protect  it  from  the  warmer  air.  B  is  a 
galvanized  iron  vessel,  21  cm.  high  and  15  cm.  wide, 
which  rests  upon  a  tripod  to  diminish  the  surface  of  con- 
tact with  the  outer  vessel.  This  is  provided  with  a  lid. 
The  vessel  B  is  completely  surrounded,  except  above, 
with  a  freezing-mixture  of  ice  and  a  little  salt.  The 
space  between  A  and  B,  filled  with  the  freezing-mixture, 
was  covered  with  a  ring  of  asbestos,  aa,  to  protect  the 
freezing-mixture  from  the  air.  C  is  a  glass  vessel,  18 
cm.  high,  10  cm.  wide,  and  of  about  1200  cc.  capacity. 
This  rests  on  a  thick  felt  bottom,  which  protects  it  from 
the  metal  vessel  beneath.  The  space  between  B  and  C  is 
filled  with  air  and  covered  above  with  a  ring  of  felt, 
bb,  which  rests  on  a  metallic  shelf  fastened  on  to  the 
inner  side  of  the  vessel  B.  The  air-chamber  between 
B  and  C  is  thus  closed  and  remains  at  nearly  the  same 
temperature  during  a  determination.  The  glass  ves- 
sel was  covered  with  a  glass  lid.  D  is  a  thermometer 
whose  bulb  is  14  cm.  in  length  and  1.5  cm.  in  width.  The 
fine  capillary  was  carefully  calibrated.  The  entire  scale, 

1  Ber.d.  chera.  Ges.,  a6,  797,  (1893);  Wied.  Ann.,  51,  500. 

2  Ztschr.  phys.  Chem.,  15,  681  (1894). 
'  Compt.  Rend.,  12a,  668  (1896). 

*  ztschr.  phys.  Chem.,  11,  no,  529  (1863). 


20 


THE  I^REKZING-POINT    METHOD 


which  was  22  cm.  in  length,  corresponded  to  only  0.6°.  It 
was  divided  into  tenths,  hundredths,  and  thousandths  of 
a  degree.  The  finest  divisions  could  be  estimated  to 
tenths,  by  means  of  a  telescope,  so  that  the  scale  could  be 
read  to  0.000 1  of  a  degree.     The  thermometer  was  of 


Fig.  3. 

the  Beckmann  type,  and  the  freezing-point  of  the  sol- 
vent could  be  adjusted  wherever  desired  upon  the  scale. 
It  was  fastened  firmly  into  the  cork  c,  and  passed  loosely 
through  g,  being  suspended  in  the  liquid  in  C. 

E  is  a  stirrer,  which  was  constructed  as  follows:  A 
circular  piece  of  sheet-silver  was  cut  slightly  smaller 
than  the  glass   vessel,   and  plated   electrolytically   with 


THE   FREEZING-POINT    METHOD 


21 


gold.     This  was  cut  along  the  circular  lines  shown  in 
Fig.  4,  and  also  horizontally,  as  indicated.     The  ends 


Fig.  4. 

marked  o  were  bent  upwards,  those  marked  u  down- 
wards. S  is  a  small  hole  which  received  the  handle.  P 
is  a  large  hole  in  the  center,  through  which  the  bulb  of 
the  thermometer  passes.     In  Fig.  5  is  given  a  section 


-fl5 


Fig.  5- 


across  one  of  the  openings,  to  show  how  the  ends  are 
cut  and  bent.  This  section  corresponds  to  the  dotted 
line  a,  h,  in  Fig.  4. 

A  stirrer  of  this  form  has  the  advantage  that  at  every 
movement  up  and  down  the  liquid  is  moved  horizontally 
and  vertically,  and  any  currents  set  up  during  the  stroke 
in  one  direction  are  completely  reversed  by  the  opposite 
stroke. 

The  advantage  claimed  for  this  method  of  work  is  that 
by  using  a  large  volume  of  the  solution  the  temperature 
3 


22  the:   freezing-point    METHOD 

can  be  much  better  regulated.  The  comparatively  thick 
layer  of  air  at  constant  temperature  around  the  inner- 
most vessel,  makes  it  far  less  susceptible  to  the  influ- 
ence of  changes  in  the  temperature  of  surrounding  ob- 
jects. The  large  volume  of  the  liquid  exposes  rela- 
tively less  surface  to  the  cooling  mixture,  and  the  rate  of 
cooling  is  comparatively  slow.  This  makes  it  possible 
to  determine  more  accurately  the  temperature  of  the 
liquid  in  which  the  ice  separates.  Since  the  rate  of 
cooling  is  slow,  the  ice  that  separates  during  the  time 
required  for  the  thermometer  to  become  constant,  is 
relatively  small. 

A  liter  of  pure  water  is  placed  in  the  vessel  C,  and  its 
freezing-point  determined  on  the  thermometer.  A  cer- 
tain volume  of  this  is  then  removed,  and  an  equal  vol- 
ume of  a  solution  of  known  concentration,  added.  Thus 
the  volume  of  the  solution  in  the  vessel  always  remains 
a  liter,  which  facilitates  the  calculation  of  the  results. 
The  same  process  is  repeated  in  making  successive  di- 
lutions. By  this  method  of  work  the  first  solution  of  a 
series  is  the  most  dilute,  and  the  solutions  become  more 
and  more  concentrated  to  the  end  of  the  series. 

Such  accuracy  as  is  obtainable  with  this  apparatus  is 
not  necessary  for  laboratory  practice,  but  is  very  desir- 
able where  the  problem  of  the  measurement  of  electro- 
lytic dissociation  presents  itself. 

The  applicability  of  the  method  to  the  problem  of  elec- 
trolytic dissociation  will  be  seen  by  comparing  the  values 
of  the  dissociation  of  a  number  of  acids,  bases,  and  salts, 
as  obtained  by  it,^  with  the  dissociation  as  determined  by 
the  conductivity  method  of  Kohlrausch.^ 

»  Ztschr.  phys.  Chem.,  la,  639  (1893). 
2  Wied.  Ann.,  26,  161  (1885). 


THE   IPREEZING-POINT    METHOD 


23 


Dissociation  Dissociation  from 

from  lowering  of 

Concentration  conductivity,  freezing-point. 

Substance.         normal.  Percent.  Percent. 

NaCl  -r o.ooi  98.0  98.4 

o.oio  93.5  907 

o.ioo  84.1  83.5 

K2SO4 0.002  92.2  94.1 

O.OIO  85.8  88.2 

O.IOO  70.1  72.0 

BaCl2 0.002  93.9  941 

O.OIO  87.9  88.4 

O.IOO  75.3  76.8 

HCl   0.002  loo.o  98.4 

O.OIO  98.9  95.8 

O.IOO  93.9  88.6 

HjSO^ 0.003  89.8  86.0 

0.005  85.4  83.8 

0.050  62.3  60.7 

HNO3    <^oo2  loo.o  98.4 

O.OIO  98.5  96.8 

O.IOO  93.5  87.8 

H3PO4 0.002  87.8  85.2 

O.OIO  63.5  68.8 

KOH 0.002  loo.o  98.4 

O.OIO  99.2  93.7 

O.IOO  92.8  83.1 

NaOH 0.002  98.9  98.4 

O.OIO  99.5  93-7 

0.050  90.4  88.4 

An  absolute  agreement  between  the  dissociation  values 
obtained  by  the  conductivity  method  and  by  the  freezing- 
point  method,  is  not  to  be  expected,  since  the  former 
method  was  used  at   18°  or  25°,  while  the  latter  was 


24  THie  FlueEZING-POINT   METHOD 

applied  at  about  o° ;  and  further,  the  hydration  of  the 
dissolved  substance  produces  a  greater  effect  upon  the 
results  of  the  freezing-point,  than  upon  the  results  of 
the  conductivity  method,  as  has  been  shown  by  Jones 
and  Pearce.^ 

1  Amer.  Chem.  Journ.,  38,  683  (1907). 


PART  IL 


THE  BOILING-POINT  METHOD 


THEORETICAL 

The  presence  of  a  foreign,  non-volatile  substance 
diminishes  the  vapor  pressure  of  the  solvent  in  which  it 
is  dissolved.  Since  the  boiling-point  of  a  solvent,  or  of 
a  solution,  is  the  temperature  at  which  the  vapor-pres- 
sure just  overcomes  the  pressure  of  the  atmosphere,  it 
follows  that  the  solution  having  a  lower  vapor-pressure 
than  the  solvent,  will  have  a  higher  boiling-point. 

There  are  thus  two  quantities,  either  of  which  we  may- 
measure  :  The  depression  of  the  vapor-tension  of  the  sol- 
vent, caused  by  the  presence  of  the  dissolved  substance; 
or  the  rise  in  the  boiling-point  of  the  solvent,  due  to  the 
same  cause. 

Passing  over  the  work  of  Faraday,  Griffiths,  Legrand, 
and  others,  along  this  line,  since  it  all  failed  to  give  any 
very  important  generalization,  we  come  to  that  of  von 
Babo,^  who  found  that  the  relation  between  the  amount 
of  salt  present  and  the  diminution  of  the  vapor-pressure, 
was  independent  of  the  temperature. 

The  work  of  Wiillner^  w^as  of  greater  significance.  He 
measured  the  depression  of  the  vapor-pressure  of  water 
especially  by  salts,  and  arrived  at  the  conclusion  that 
the  diminution  of  the  vapor-pressure  of  water,  pro- 
duced by  dissolved,  non-volatile  substances,  was  pro- 
portional to  the  amount  of  substance  present. 

1  Jahrb.  Chem.,  1848-49,  93  ;  1857,  72. 

«  Fogg.  Ann.,  103,  529,  (1858);  105,  85  (1858). 


26  THE    BOIUNG-POINT    METHOD 

While  this  is  true  only  in  certain  cases,  or  indeed  only 
for  certain  classes  of  compounds,  yet  it  is  strictly  analo- 
gous to  the  earliest  generalization  reached  in  connection 
with  the  study  of  the  depression  of  the  freezing-point  of 
a  solvent  by  a  foreign  substance.  It  will  be  remembered 
that  Blagden  stated  that  the  depression  of  the  freezing- 
point  of  a  solvent  by  a  dissolved  substance  was  propor- 
tional to  the  amount  of  substance  present. 

When  depressions  of  the  freezing-point  were  measured 
with  a  fair  degree  of  accuracy,  it  was  shown  that  the 
generalization  of  Blagden  held  only  approximately,  and 
ill  some  cases.  So  also,  the  relation  pointed  out  by 
Wiillner  was  shown  by  the  work  of  Pauchon,^  Tam- 
mann^  and  Emden^,  to  be  only  an  approximation  under 
certain  conditions. 

It  is  to  Raoult  more  than  to  any  other  investigator  that 
we  owe  the  theoretical  development  of  the  subject  in 
hand. 

He  employed  the  first  of  the  two  quantities  men- 
tioned, and  measured  the  depression  of  the  vapor-tension 
of  a  solvent  by  foreign  substances.  A  number  of  rela- 
tions were  brought  out  by  him  from  a  study  of  solutions 
in  solvents  other  than  water,  which  would  not  have  been 
discovered  in  aqueous  solutions,  since  these  are  often  dis- 
sociated, and  to  a  different  amount  for  different  dilutions. 

Raoult*  confirmed  the  generalization  of  von  Babo, 
that  the  relation  between  the  depression  of  the  vapor- 
pressure  and  the  vapor-pressure  of  the  solvent,  was  in- 
dependent of  the  temperature  between  o°  and  20°.  Also 
that  of  Wiillner,  that  the  depression  of  the  vapor-pres- 

1  Compt.  Rend.,  89,  752  (1879). 

«  Wied.  Ann.,  24,  523  (1885). 

87*1^,31,145(1887). 

*  Compt.  Rend.,  103,  1125  (1886). 


THE    EOIUNG-POINT    METHOD  27 

sure  was  proportional  to  the  concentration  (when  there 
was  no  dissociation). 

If  we  represent  the  vapor-pressure  of  the  pure  solvent 
by  p,  and  that  of  the  solution  by  />', 

P-P' 
P 

is  independent  of  the  temperature  and  proportional  to 
the  concentration. 

The  nature  of  the  substance  used  was  then  investi- 
gated to  determine  whether  the  chemical  composition  of 
the  molecule  had  any  effect  on  its  power  to  depress  the 
vapor-tension. 

Solutions  containing  the  same  number  of  molecules  of 
different  substances  in  solution  in  the  same  number  of 
molecules  of  a  given  solvent,  must  be  compared  as  to 
their  vapor-pressures.  This  would  be  difficult  to  carry 
out  directly.  Convenient  concentrations  of  different 
substances  were  used,  the  vapor-pressures  of  the  solu- 
tions determined,  and  the  molecular  depression  of  the 
vapor-pressure  calculated  for  each  substance  from  the 
expression — 

P-P\,  ^ 

p        g 

in  which  m  is  the  molecular  weight  of  the  substance, 
and  g  the  number  of  grams  in  100  grams  of  the  solvent. 

He  found  that  the  molecular  depression  of  the  vapor- 
pressure  of  a  solvent  is  a  constant  for  a  given  solvent, 
independent  of  the  nature  of  the  substance  which  is  dis- 
solved in  it.  This  holds,  as  we  now  know,  only  when 
the  dissolved  substances  are  undissociated  by  the  solvent. 

Raoult^   investigated  also  the   relative  diminution  of 

1  Compt.  Rend.,  104,  1430  (1887). 


28  THE    BOII<ING-POINT    METHOD 

the  vapor-pressure  of  different  solvents,  when  the  rela- 
tion between  the  number  of  molecules  of  the  substance 
and  that  of  the  solvent  was  the  same. 
•  Below  are  given  the  results  of  the  relative  diminution 
of  the  vapor-pressure  for  twelve  solvents,  calculated  on 
the  basis  of  one  molecule  of  the  substance  to  loo  mole- 
cules of  the  solvent : 

Water 0.0102 

Phosphorus  trichloride    0.0108 

Carbon  disulphide 0.0105 

Tetrachlormethane 0.0105 

Chloroform 0.0109 

Amylene 0.0106 

Benzene 0.0106 

Methyl  iodide 0.0105 

Methyl  bromide 0.0109 

Ether 0.0096 

Acetone o.oioi 

Methyl  alcohol 0.0103 

The  relative  diminution  of  the  vapor-pressure  of  sol- 
vents, produced  by  a  molecule  of  a  non-volatile  sub- 
stance, in  the  same  number  of  molecules  of  the  sol- 
vents, is  very  nearly  a  constant.  This  relation  has  been 
satisfactorily  formulated  thus — 

p  N  ^7l' 

in  which  n  is  the  number  of  molecules  of  the  dissolved 
substance,  N  that  of  the  solvent,  and  c  a  constant 
which,  from  the  foregoing  table,  can  be  regarded  as 
unity.     The  expression  becomes  then — 

P-P  ^       n 

p  N^n  ' 

or  the  lowering  of  the  vapor-pressure  of  the  solvent  is 


THE    BOIUNG-POINT    METHOD  29 

to  the  vapor-pressure  of  the  solvent,  as  the  number  of 
molecules  of  the  dissolved  substance  is  to  the  entire 
number  of  molecules  present.  This  expression  was 
tested  experimentally  by  Raoult/  and  found  to  hold  for 
a  large  number  of  substances  in  ethereal  solution. 

From  the  foregoing  it  will  be  seen  that  the  molecular 
weight  of  substances  can  be  determined  directly  from  the 
depression  of  the  vapor-pressure  of  a  solvent  which  they 
produce. 

Let  the  molecular  weight  of  the  substance  be  repre- 
sented by  m,  and  the  amount  used  by  a,  then  the  num- 
ber of  molecules,  n  =  —  . 
m 

Making  A/"  =  i,  and  substituting  this  value  of  n  in 
the  expression — 

P-P'  _       n 

p  N-\-n  * 

we  have — 

p'a 

Knowing  />,  />'  and  a,  we  can  directly  calculate  m. 

As  a  practical  method  for  determining  molecular 
weights  this  is  not  used,  since  such  measurements  are 
not  easily  carried  out  and  are  not  very  accurate. 

It  has  been  found  to  be  simpler  and  more  accurate  to 
determine  the  temperature  at  which  the  vapor-pressure 
of  the  solution  is  equal  to  that  of  the  solvent.  Since  the 
boiling-point  of  a  liquid  is  the  temperature  at  which  its 
vapor-pressure  just  overcomes  the  pressure  of  the  atmo- 
sphere, the  boiling-points  of  a  solvent  and  of  a  solution  in 
that  solvent  are  the  temperatures  of  equal  vapor-pres- 

1  Ztschr.  phys.  Chem.,  2,  371  (1888). 


30  the;  boiung-point  method 

sures.  The  object  is  then  to  determine  the  rise  in  the 
boiling-point  of  a  solvent  produced  by  the  substance  dis- 
solved in  it. 

The  experimental  method  for  carrying  out  such  de- 
terminations we  owe  to  Beckmann.  The  forms  of  appara- 
tus which  seem  best  adapted  to  this  work,  and  the  details 
of  an  experiment  will  be  considered  in  the  second  part 
of  this  chapter. 

The  rise  in  the  boiling-point  is  directly  proportional 
to  the  lowering  of  the  vapor-pressure,  and  depends  upon 
the  relative  number  of  molecules  of  the  solvent  and  of  the 
dissolved  substance. 

The  probability  of  calculating  molecular  weights 
directly  from  the  rise  in  the  boiling-point  of  solvents 
produced  by  substances  dissolved  in  them,  is  at  once  ap- 
parent. 

The  expression  by  which  the  molecular  weights  are 
calculated,  is  analogous  to  that  already  given  for  calcu- 
lating molecular  weights  from  lowerings  of  the  freezing- 
point  of  solvents  by  dissolved  substances.  If  we  repre- 
sent the  unknown  molecular  weight  by  w,  the  weight  of 
the  substance  taken  by  s,  the  weight  of  the  solvent  used 
by  ►S',  and  the  rise  produced  in  the  boiling-point  of  the 
solvent  by  R,  we  have — 

C  s 

in  which  C  is  a  constant  of  different  value  for  each  sol- 
vent. 

The  analogy  between  the  lowering  of  the  freezing- 
point  and  the  rise  in  the  boiling-point  holds  still  further, 
in  that  the  value  of  C  can  be  calculated  from  the  same 
formula : — 


THE    BOII.ING-POINT    METHOD  3 1 

100  L 

When  applied  to  calculating  the  constant  for  the  boil- 
ing-point method  of  determining  molecular  weights,   T 

is  the  absolute  temperature  at  which  the  pure  solvent 

boils  and  L  the  heat  of  vaporization  of  the  solvent. 

The  values  of  C  /or  a  number  of  the  solvents  more 
commonly  used,  are  given  below. 

Boiling-point  Constant 

Acetic  acid 118.0  25,3 

Acetone 56.3  16.7 

Ammonia — 33.7  3.2 

Amylalcohol  (/56>) 131. 5  25.75 

Aniline 184.0  32.2 

Anizol 155.0  44.3 

Benzene 80.3  26.7 

Benzonitrile 191. o  36.5 

Bromine 63.0  52.0 

Chloroform 61.2  36.6 

Carbon  disulphide 46.2  23.7 

Carbon  tetrachloride • .       78.5  48.0 

Ethyl  acetate 75.5  27.9 

Ethyl  alcohol 78.8  11. 5 

Ethyl  bromide 37.7  25.3 

Ethylene  bromide 130.0  64.3 

Ethyl  ether 35.0  21. i 

Formic  acid 100.6  34.0 

Isobutyl  alcohol 104.6  19,4 

Mercury 357.0  130.0 

Methyl  acetate 56.5  20.6 

Methyl  alcohol 67.0  8.4 

Methyl  formate 32.3  15.05 

Methyl  iodide 41.3  41.9 

Nitrobenzene    205.0  50.1 

Paraldehyde 123.0  41.8 

Phenol 183.0  30.4 

Propyl  alcohol 94.8  15.8 

Pyridine 115. o  30.1 

Water loo.o  5.2 


32  THE   BOIUNG-POINT    METHOD 

Some  of  the  relations  between  the  boiling-point  and 
the  freezing-point  methods  have  been  mentioned,  but 
others,  however,  exist.  It  will  be  remembered  that  the 
freezing-point  method  can  be  used  to  determine  the 
molecular  weights  of  only  a  limited  number  of  sub- 
stances— ^the  non-electrolytes.  The  boiling-point  method 
is  subject  to  the  same  limitation.  Those  substances 
that  give  abnormally  great  depressions  of  the  freezing- 
point,  due  to  electrolytic  dissociation,  give  abnormally 
great  depressions  of  the  vapor-tension,  or  rise  in  the 
boiling-point.  It  was  pointed  out  that  in  such  cases  the 
freezing-point  method  could  be  used  to  measure  the 
amount  of  dissociation  in  the  solutions.  The  boiling- 
point  method  may  be  used  for  the  same  purpose,  but 
is  not  capable  of  the  same  degree  of  accuracy  as  the 
freezing-point  method. 

Some  recent  work,^  however,  has  shown  that  it  can 
be  applied  to  the  problem  of  electrolytic  dissociation  in 
solution,  and  when  all  the  indicated  precautions  are 
taken,  it  is  capable  of  giving  fairly  satisfactory  results. 

The  Application  of  the  Boiling-Point  Method  to  the 
Determination  of  Molecular  Weights  in  Solution 

The  precautions  that  are  necessary  in  making  such 
measurements  will  be  understood  best  by  pointing  out 
the  more  prominent  sources  of  error  to  which  the  boiling- 
point  method  is  subject. 

The  method  as  such,  is  not  capable  of  that  refine- 
ment to  which  the  freezing-point  method  lends  itself. 
It  is  sensitive  to  barometric  changes,  which  seriously  af- 
fect the  boiling-points  of  liquids.     In  this  method  the 

1  Jones  and  King  :  Amer.  Chem.  Journ.,  19,  581  (1897). 


THE   EOIUNG-POINT    METHOD  33 

vapor  escapes  quickly  from  the  solution  in  which  its 
presence  is  necessary  to  establish  the  equilibrium  tem- 
perature. The  difference  in  temperature  between  the 
liquid  and  surrounding  objects  is  generally  much  greater 
in  this  method  than  in  the  freezing-point  method,  so  that 
more  precautions  are  necessary  to  protect  the  solution 
and  thermometer  from  changes  in  the  temperature  of 
external  objects.  In  this  method  a  part  of  the  com- 
paratively pure  solvent  is  constantly  separating  from  the 
solution  as  vapor,  and  is  returned  as  a  liquid,  at  a  tem- 
perature lower  than  that  of  the  boiling  solution.  The 
amount  of  this  liquid  cannot,  for  given  conditions,  be 
determined  with  the  same  degree  of  accuracy  as  was 
possible  in  ascertaining  the  amount  of  ice  that  separated 
in  the  freezing  liquid.  The  large  Beckmann  thermom- 
eters are  more  liable  to  undergo  change  at  the  compara- 
tively high  temperatures  to  which  they  are  subjected  in 
this  method,  than  in  the  freezing-point  method,  where  the 
temperature  of  the  thermometer  is  at  no  time  widely  re- 
moved from  the  ordinary.  The  boiling-point  method  has 
this  advantage  that  more  solvents  can  be  employed,  since 
comparatively  few  solvents  freeze  within  the  ordinary 
range  of  temperatures ;  and  further,  the  solubility  of  sub- 
stances is  generally  increased  at  the  higher  temperatures. 
It  is,  on  the  other  hand,  a  misfortune  for  the  boiling- 
point  method  that  aqueous  solutions  cannot  be  used  satis- 
factorily, partly  because  of  the  very  small  constant  for 
water. 

A  number  of  forms  of  apparatus  for  determining  the 
boiling-points  of  solvents  and  solutions  have  been  de- 
vised by  Beckmann,^  to  whom  we  are  as  much  indebted 
for  the  experimental  development  of  the  subject  as  we 

1  Ztschr.  phys.  Chem.,  4,  544  (18S9);  8, 224  (1891);  15, 663,  (1894);  ai,  246  (1856). 


34 


THE    BOILING-POINT    METHOD 


are  to  Raoult  for  its  theoretical.  That  one,  which 
judged  by  the  results/  seems  to  be,  on  the  whole,  the 
most  satisfactorily,  is  seen  in  Fig.  6.     The  inner  glass 


Fig.  6. 


vessel  A,  provided  with  a  return  condenser  K,  receives 
the  liquid  whose  boiling-point  is  to  be  determined. 
The  bottom  of  this  vessel  is  filled  to  a  depth  of  a  few 

1  Ztschr.  phys.  Chem.,  8,  224  (1891). 


TH]^   BOIWNG-POINT    METHOD  35 

centimeters  with  glass  beads  or  small  garnets,  so  that 
the  boiling  may  take  place  simultaneously  from  a  number 
of  points  and  proceed  more  smoothly.  The  bulb  of  the 
Beckmann  thermometer  is  placed  well  below  the  surface 
of  the  liquid.  Tube  A  is  surrounded  on  the  sides  with 
a  double- walled  glass  jacket  B,  into  which  some  of  the 
same  solvent  placed  in  A  is  introduced.  The  object  is 
to  surround  the  boiling  liquid  with  a  liquid  as  nearly  at 
its  own  temperature  as  possible.  This  jacket  is  provided 
with  a  return  condenser  K2.  The  whole  is  supported  on 
a  box  of  asbestos  C,  which  is  open  beneath.  Heat  is  ap- 
plied as  shown  in  the  drawing. 

The  results  obtained  by  Beckmann^  with  the  use  of 
this  apparatus  were  very  good.  It  is,  however,  not  free 
from  objections.  It  is  certain  that  the  eiffect  of  radia- 
tion from  the  bulb  of  the  thermometer  outward  upon  the 
colder  objects,  was  not  entirely  cut  off  by  the  form  of 
jacket  employed.  Beckmann^  used  in  a  later  form  a 
porcelain  jacket,  having  abandoned  a  metallic  one, 
which  doubtless  cuts  off  the  radiation  more  effectively 
than  the  one  of  glass.  But  an  objection  which  applies 
to  every  form  of  apparatus  devised  by  Beckmann,  is  that 
the  cold  solvent  from  the  condenser  is  returned  directly 
into  the  hot  liquid  into  which  the  thermometer  is  immers- 
ed. That  the  thermometer  is  affected  by  this,  in  that 
it  tends  to  lag  behind  the  true  boiling-temperature  of  the 
liquid,  is  certain. 

A  form  of  apparatus  which  largely  eliminates  this 
latter  source  of  error,  was  devised  by  Hite,^  and  is 
shown  in  Fig.   7.       The   distinctive  advance  made  by 

»  Ztschr.  phys.  Chem,,  8,  226  (iigi). 

2 /*lrf,  15,662(1894). 

3  Amer.  Chem.  Journ.,  17,  514  (1895). 


36  THE    EOIUNG-POINT    MEiTHOD 

Hite  is  the  introduction  of  an  inner  glass  tube,  which 
prevents  the  condensed  solvent  from  coming  in  contact 
with  the  thermometer  before  it  is  reheated  to  the  boil- 
ing-point. The  cooled  liquid  must  pass  through  a  layer 
of  the  boiling  liquid  between  the  walls  of  the  inner  and 
outer  vessel,  some  centimeters  deep,  before  it  can  enter 
the  inner  tube  which  receives  the  thermometer.  The 
inner  vessel  is  closed  at  the  bottom  by  means  of  a  glass 
stopper.  Grooves  are  filed  into  the  edge  of  the  stop- 
per to  allow  the  vapor  to  stream  through  into  the  inner 
vessel  in  fine  bubbles,  and  stir  the  liquid  around  the 
thermometer.  I  am  inclined  to  lay  rather  less  stress 
upon  the  importance  of  this  device,  than  upon  the 
separation  of  the  condensed  solvent  from  the  liquid  in 
which  the  thermometer  is  placed,  until  it  has  been  re- 
heated to  the  boiling-point.  The  apparatus  gave  ad- 
mirable results  with  low-boiling  solvents,  but  could  not 
be  used  for  solvents  which  boil  over  ioo°. 

The  present  writer^  has  devised  a  form  of  apparatus 
which  aims  both  at  reducing  to  a  minimum  the  error 
from  radiation,  and  at  preventing  the  condensed  solvent 
from  coming  in  contact  with  the  thermometer  until  it  is 
reheated  to  the  boiling-point.  It  is  also  one  of  the  sim- 
plest of  the  efficient  forms  thus  far  devised.  It  is  shown  in 
section  in  Fig.  8.  A  is  a  glass  tube  i8  cm.  high  and  4 
cm.  in  diameter,  drawn  out  at  the  top  to  a  diameter  of 
about  2^  cm.  and  ground  to  receive  a  ground-glass  stop- 
per. This  tube  is  filled  to  a  depth  of  from  3  to  4  cm. 
with  glass  beads.  P  is  a  cylinder  of  platinum,  8  cm. 
high  and  23^  cm.  in  width,  made  by  rolling  up  a  piece  of 
platinum  foil,  and  fastening  it  in  position  by  wrapping  it 
near  the  top  and  bottom  with  platinum  wire.     Into  the 

1  Amer.  Chem.  Journ.,19,  581  (1897). 


p 


Fig.  7. 


Fig.  8. 


38  THE    BOIUNG-POINT    METHOD 

cylinder  P,  some  pieces  of  platinum  foil  are  thrown. 
These  are  made  by  cutting  foil  into  pieces  about  ^  cm. 
square,  bending  the  corners  alternately  up  and  down,  to 
prevent  them  from  lying  too  closely  upon  one  another, 
and  serrating  the  edges  with  scissors,  to  give  a  greater 
number  of  points  from  which  the  boiling  can  take  place. 
The  bulb  of  the  thermometer  is  thus  entirely  surrounded 
except  directly  above  by  metal  at  very  nearly  its  own 
temperature.  A  condenser  C,  about  40  cm.  in  length, 
is  attached  to  the  tube  Aj,  which  is  2  or  2>4  cm.  in  di- 
ameter, by  means  of  a  cork.  When  it  is  desired  to  pro- 
tect the  solvent  from  the  moisture  in  the  air,  the  top  of 
the  condenser  tube  should  be  provided  with  a  tube  con- 
taining calcium  chloride  or  phosphorus  pentoxide.  Dur- 
ing an  experiment,  the  vessel  A  is  closed  above  by  a  cork, 
through  which  the  Beckmann  boiling-point  thermometer 
T  passes.  M  is  a  jacket  of  asbestos,  12  cm.  high  and 
i^  cm.  thick,  over  the  top  of  which  the  rate  of  boiling 
can  be  satisfactorily  observed.  It  is  constructed  by 
bending  a  thin  board  of  asbestos  tightly  around  the 
tube  A,  and  fixing  it  in  place  by  means  of  a  copper 
wire.  Thick  asbestos  paper  is  then  wound  around  this 
until  the  desired  thickness  is  reached.  The  apparatus 
is  supported  on  a  small  iron  tripod  S,  8  cm.  in  diameter, 
on  which  rests  an  asbestos  ring  R,  about  9  cm.  in  exter- 
nal diameter.  A  circular  hole  is  cut  in  the  center  of 
this  ring,  about  35^  cm.  in  diameter,  and  over  this  is 
placed  a  piece  of  fine  copper  gauze.  The  source  of  heat 
is  a  Bunsen  burner  B,  surrounded  by  an  ordinary  metal- 
lic cone  I,  to  protect  the  small  flame  from  air-currents. 
The  glass  vessel  A  is  shoved  down  until  it  comes  in 
contact  with  the  wire  gauze.     Under  these  conditions  a 


THE    BOILING-POINT    METHOD  39 

very  small  flame  suffices  when  low-boiling  solvents  are 
employed,  and  not  a  large  flame  is  required  when  a  sol- 
vent like  aniline  is  used, 

A  number  of  other  forms  of  apparatus  have  been  con- 
structed for  determining  the  boiling-points  of  liquids, 
but  these  cither  do  not  sufficiently  eliminate  sources  of 
error  for  accurate  work,  or  are  so  complex  that  they  can 
scarcely  hope  to  find  general  application  in  the  labora- 
tory for  the  purpose  of  determining  molecular  weights. 

Carrying  Out  a  Determination 

The  thermometer  must  first  be  so  adjusted  that  the 
top  of  the  mercury  thread  comes  to  rest  on  the  lower 
half  of  the  scale,  when  the  bulb  is  immersed  in  the  boil- 
ing solvent.  This  is  accomplished  by  placing  some 
glass  beads  in  cylinder  A,  and  adding  the  pure  solvent 
until  the  bulb  of  the  thermometer  will  be  covered  when 
inserted  in  place.  The  solvent  is  then  boiled,  and  as 
much  mercury  as  possible  is  driven  out  of  the  lower  bulb 
into  the  upper  cup.  The  thermometer  is  then  removed 
from  the  liquid,  inverted  for  a  few  moments,  when  still 
more  of  the  mercury  in  the  bulb  will  run  down  into  the 
cup.  The  thermometer  is  then  quickly  brought  into 
normal  position  and  given  a  sudden  tap,  when  the  mer- 
cury will  fall  from  the  top  to  the  bottom  of  the  cup  and 
leave  the  column  free.  The  bulb  is  again  placed  in  the 
boiling  solvent,  and  if  the  thread  comes  to  rest  where  de- 
sired, the  apparatus  is  ready  for  a  determination.  If  not, 
the  process  must  be  repeated  until  the  desired  result  is 
reached,  which,  however,  does  not  usually  require  any 
considerable  expenditure  of  time. 

When  the  thermometer   is   adjusted,   it  must  be   re- 


40  THE    EOII.ING-POINT    METHOD 

moved,  and  the  apparatus  and  beads  entirely  freed  from 
the  liquid.  The  glass  beads  are  then  poured  into  the 
glass  cylinder,  the  platinum  cylinder  inserted,  and 
pressed  down  into  the  beads  to  a  distance  of  from  >4  to  i 
cm.  The  platinum  plates  are  then  introduced  into  the 
platinum  cylinder,  the  end  of  the  tube  A,  closed  with  a 
cork,  and  the  ground-glass  stopper  inserted  into  A. 
The  apparatus  is  then  set  into  a  small  beaker  glass  and 
weighed,  the  solvent  introduced,  and  the  whole  re- 
weighed.  Great  care  must  be  taken  that  not  enough  of 
the  solvent  is  employed  to  boil  over  from  the  inside  of 
the  platinum  cylinder  to  the  outside.  In  case  a  labora- 
tory is  not  provided  with  a  balance  capable  of  weighing 
accurately  200  or  300  grams,  the  solvent  must  be  weighed 
directly  and  poured  into  the  apparatus.  This  method  of 
procedure,  for  low-boiling  solvents,  is  necessarily  less  ac- 
curate, due  to  loss  by  evaporation. 

After  the  solvent  is  weighed  the  glass  stopper  is  re- 
moved, and  the  thermometer,  fitted  tightly  into  a  cork,  is 
placed  in  position,  as  shown  in  the  drawing.  The  appa- 
ratus is  then  placed  upon  the  stand  in  the  mantle  of  asbes- 
tos, the  cork  removed  from  A,  and  the  condenser  at- 
tached. Heat  is  then  applied  and  the  solvent  boiled. 
The  size  of  the  flame  must  be  so  regulated  by  means  of 
a  screw  pinch-cock,  that  the  boiling  is  quite  vigorous, 
but  not  so  violent  as  to  be  of  an  irregular  or  explosive 
character.  A  quiet  but  very  active  boiling  is  absolutely 
essential  to  the  success  of  the  experiment.  The  time 
required  to  establish  the  true  temperature  of  equilibrium 
between  the  pure  liquid  solvent  and  its  vapor,  is 
much  greater  than  in  the  case  of  a  solution.  This  is 
strictly  analogous  to  what  is  observed  with  the  freezing- 


THIS    BOIUNG-POINT    METHOD  4I 

point  method.  Here  the  time  necessary  to  establish 
the  temperature  of  equilibrium  between  the  solid  and 
liquid  phases  of  the  pure  solvent,  is  always  much  greater 
than  for  a  solution.  Before  taking  a  reading  on  the 
Beckmann  thermometer,  it  is  always  necessary  to  give 
it  a  few  sharp  taps  with  a  lead  pencil,  and  indeed  this 
should  be  done  occasionally  while  the  mercury  is  rising, 
and  especially  when  it  is  near  the  point  of  equilibrium. 
The  use  of  an  electric  hammer  to  accomplish  this  object 
is  an  unnecessary  complication.  A  small  hand-lens, 
magnifying  a  half  dozen  times,  is  quite  sufficient  to  use 
in  making  the  readings.  It  is  always  best  to  redetermine 
the  boiling-point  of  the  solvent.  After  this  point  has  been 
ascertained,  a  tube  containing  the  substance  pressed  into 
pellets,  whose  molecular  weight  it  is  desired  to  determine, 
is  weighed,  and  a  convenient  number  of  these  poured 
into  the  solvent,  either  through  the  condenser  or  directly 
through  the  tube  A  when  the  solvent  is  not  too  volatile 
and  has  ceased  to  boil.  The  tube  is  then  reweighed, 
and  the  amount  of  substance  introduced,  thus  ascertained. 
The  boiling-point  of  the  solution  is  then  determined. 

The  carrying  out  of  a  determination  with  a  low-boil- 
ing solvent  is  a  much  easier  process  than  with  one  boil- 
ing at  a  considerably  higher  temperature. 

Thus;  when  anisol  or  aniline  is  employed,  much  care 
and  some  experience  are  necessary  to  determine  the  rate 
of  boiling  which  must  be  adopted.  If  the  boiling  is  too 
slow,  the  thermometer  will  never  reach  the  temperature 
of  equilibrium ;  if  so  rapid  that  it  is  irregular  and  explo- 
sive, the  thermometer  may  rise  above  the  true  point,  and 
then  suddenly  drop  below  it  at  the  moment  when  a  large 
amount  of  the  vapor  is  set  free.     In  a  word,  for  high- 


42  THE    BOILING-POINT    METHOD 

boiling  solvents  the  rate  of  boiling  must  be  as  vigorous 
as  possible,  in  order  to  proceed  with  perfect  regularity. 

In  all  such  determinations  the  barometer  must  be  care- 
fully observed;  but  after  the  boiling-point  of  the  sol- 
vent has  been  determined,  that  of  the  solution  can  be  as- 
certained so  quickly  that  the  changes  in  the  barometer 
during  this  short  interval  are  usually  so  slight  that  they 
are  negligible.  Whenever  they  are  of  appreciable  value, 
a  correction  must  be  accordingly  introduced.  The  cor- 
rection for  methyl  and  ethyl  alcohols  is  0.004°  for  o.i 
mm.  change  in  the  barometer. 

A  portion  of  the  nearly  pure  solvents  is  constantly  evap- 
orating from  the  solution,  and  condensing  on  the  walls 
of  the  apparatus  itself  and  in  the  condenser.  The  solu- 
tion is  thus  more  concentrated  than  would  be  calculated 
from  the  amount  of  substance  and  of  solvent  used.  A 
correction  must  be  introduced  for  the  amount  of  the  sol- 
vent which  separates  from  the  solution,  as  was  neces- 
sary in  the  freezing-point  method.  Unfortunately,  we 
cannot  determine  the  amount  in  the  boiling-point  method 
with  even  the  same  degree  of  accuracy  as  in  the  freez- 
ing-point method. 

The  amount  of  the  solvent  which  exists  under  ordinary 
conditions,  as  vapor  and  condensed  liquid,  is  given  by 
Ostwald^  as  0.2  gram,  and  0.35  gram  of  water.  But 
this  evidently  must  be  taken,  as  only  a  rough  approxima- 
tion. 

Thus  all  the  data  are  at  hand  for  calculating  the  molecu- 
lar weight  of  the  substance  in  the  solvent  used,  from 
the  formula  already  given  (page  30)  : 

1  Hand  und  Hilfsbuch  zur  Ausfuhrung  Physiko-Chemischer  Messungen, 
p.  224. 


THE    BOIUNG-POINT    ME^THOD  43 

Cw 

"'  =  -rW 

Below  are  given  a  few  of  the  results  obtained  with  my 
apparatus  for  solvents  boiling  from  34.9°  to  182.5°. 

Soi,vKNT,  Ether  :  ^^  =  2110  ;  Boiwng-Point,  34.9°  at  760  mm. 
Naphthalene,  128. 

FIRST  SERIES. 

Ether.         Naphthalene         Rise  in  Molecular 

Grams.  Grams.        boiling-point.       weight. 

1 57.573  1-2365  0.357°  126.9 

2 57.573  2.5155  0.716°  128.8 

3 57.573  3.8733  i.iio**  127.9 

Mean,  127.9 

Soi,vENT,  Benzene:  /&  =  267o;  Boiwng-Point,  80.36°  at 
760  mm. 

Naphthalene,  128. 

Benzene.        Naphthlene.  Rise  in  Molecular 

Grams.  Grams.        boiling-point.       weight. 

1  70.560  0.7594  0.215°  133.7 

2  70..560  2.0548  0.574°  135.4 

3  70-560  3.0780  0.850°  137.0 

4  70.560  4.4790  1.234°  137.4 

Mean,  135.9 
Soi^VENT,  AN11.INE  :  ^=3220  ;  Boii^iNG-PoiNT,  182.5°  AT  738  mm. 
7  fiphenylmethane,  244. 

FIRST  SERIES. 

Aniline.  Triphenylmethane.  Rise  in  Molecular 

Grams.  Grams.        boiling-point.       weight. 

1    60.126  0.8017  0.180°  238.6 

2    60.126  1.6052  0.353°  243.5 

3    60.126  2.2914  0.496°  247.4 

4  60.126  2.9213  0.654°  239.2 

Mean,  242.2 


44  THE)    BOII.ING-POINT    METHOD 

Dipheny laming,  i6g. 

Aniline.  Triphenylmethane.  Rise  in  Molecular 

Grams.  Grams.        boiling-point.       vyeight. 

1    64.220  0.7780  0.224°  I74-I 

2  64.220      1.3326      0.391°      170.9 

3   64.220  1.7832  0.535°  167.1 

Mean,  170.7 

For  practice  in  the  laboratory  it  is  far  better  to  use 
solvents  with  low  boiling-points,  such  as  ether  or  ben- 
zene. Ethyl  alcohol  can  be  employed,  but  the  results 
are  liable  to  be  less  accurate,  since  its  constant  is  com- 
paratively small. 

Naphthalene  is  easily  obtained  pure,  and  may  be  used 
in  both  ether  and  benzene.  In  alcohol:  benzoic  acid, 
urea,  or  acetamide  may  be  conveniently  used;  while  tri- 
phenylmethane, diphenylamine  or  benzanilide,  give  good 
results  with  aniline  as  a  solvent. 

The  Application  of  the  Boiling-Point  Method   to  the 
Measurement  of  Electrolytic  Dissociation 

The  importance  of  being  able  to  apply  the  boiling- 
point  method  to  measure  the  dissociation  of  electrolytes 
in  nonaqueous  solvents  will  be  seen  from  the  following: 

Take  methyl  and  ethyl  alcohols ;  next  to  water  they  are 
probably  the  most  important  solvents  in  all  chemistry. 
Until  quite  recently  there  was  no  method  available  for 
measuring  the  dissociation  of  even  the  most  strongly 
dissociated  electrolyte  in  these  solvents.  The  conductivity 
method  could  not  be  used,  since  with  the  forms  of  cells 
then  in  use  it  was  impossible  to  determine  the  values  of 
fio.  in  these  solvents.  The  dilution  at  which  complete 
dissociation  in  these  solvents  was  reached  was  so  great, 
that  it  was  impossible  to  apply  the  conductivity  method 


THE    EOIUNG-POINT    MI^THOD  45 

to  these  dilutions  with  any  reasonable  degree  of  ac- 
curacy. 

These  solvents  are  so  frequently  used,  and  the  prob- 
lem of  the  dissociation  of  electrolytes  dissolved  in  them 
so  fundamental  to  our  scientific  knowledge  of  alcoholic 
solutions,  that  we  must  have  some  method  of  measuring 
their  dissociating  power. 

The  freezing-point  method  obviously  cannot  be  used 
with  these  solvents  because  they  freeze  at  temperatures 
that  are  far  too  low  to  measure  accurately.  Until  the 
conductivity  method  was  recently  improved  in  this  lab- 
oratory, we  were  practically  limited  to  the  boiling-point 
method  to  solve  this  problem.  The  solvents  named  above, 
and  many  others  of  great  importance  for  the  science  of 
chemistry,  boil  at  temperatures  not  so  very  widely  re- 
moved from  the  ordinary,  and  their  boiling-points  can, 
therefore,  be  accurately  determined. 

Before  the  boiling-point  method  could,  however,  be 
used  to  measure  electrolytic  dissociation,  it  must  be  im- 
proved so  as  to  eliminate  many  errors  that  were  inher- 
ent in  the  method  as  Beckmann  left  it.  Indeed,  it  was 
this  objection  especially  that  led  me  to  introduce  the 
improvements  in  the  boiling-point  method  already  re- 
ferred to. 

Measurement  of  Electrolytic  Dissociation 

The  carrying  out  oi  an  experiment  for  the  purpose  of 
measuring  electrolytic  dissociation  is  the  same  in  all  es- 
sential details  as  in  the  determination  of  the  molecular 
weight  of  a  dissolved  substance.  The  thermometer  is  so 
adjusted  as  to  bring  the  boiling-point  of  the  alcohol  near 
the  bottom  of  the  scale.    A  weighed  quantity  of  the  al- 


46  THE    BOII.ING-POINT    METHOD 

cohol  is  then  introduced  into  the  tube  and  its  boiHng-point 
determined  at  least  twice  upon  the  scale,  care  being 
taken  not  to  introduce  enough  alcohol  to  boil  over  from 
the  outside  into  the  inside  of  the  cylinder.  In  determining 
the  boiling-point  of  the  solvent  all  of  the  precautions  pre- 
viously referred  to  must  be  observed.  The  boiling  must 
be  vigorous  but  not  explosive,  the  thermometer  must  be 
tapped  to  prevent  any  sticking  of  the  mercury,  and  the 
barometer  must  be  carefully  read. 

The  substance  whose  dissociation  is  to  be  measured  is 
weighed  in  a  ground-glass  stoppered  weighing  tube,  and 
introduced  into  the  solvent  after  it  has  cooled  sufficiently. 
The  boiling-point  of  the  solution  is  then  determined  in 
the  same  manner  as  that  of  the  solvent.  The  proper  cor- 
rection for  any  change  in  the  barometer  is  applied  to  the 
rise  in  the  boiling-point  of  the  solvent  produced  by  the 
dissolved  substance,  to  get  the  true  rise  in  the  boiling- 
point;  this  correction  for  methyl  and  ethyl  alcohols  and 
solutions  in  these  solvents  is,  as  already  stated  0.004°  for 
a  barometric  change  of  o.i  mm.  of  mercury. 

Calculation  of  the  Dissociation 

The  method  of  calculating  the  dissociation  of  electro- 
lytes from  the  rise  in  the  boiling-point  of  the  solvent 
produced  by  them,  is  strictly  analogous  to  that  employed 
for  calculating  the  dissociation  of  electrolytes  from  the 
lowering  of  the  freezing-point  of  the  solvents  in  which 
they  are  dissolved. 

From  the  rise  in  the  boiling-point  observed  on  the  ther- 
mometer, the  molecular  rise  is  calculated  by  dividing  the 
observed  rise  by  the  concentration  of  the  solution  ex- 
pressed decimally.  The  concentration  is  calculated  on  the 


the:  boiung-point  method  47 

basis  of  a  gram-molecular  weight  of  the  substance  in 
one  thousand  grams  of  the  solvent.  When  the  observed 
rise  is  divided  by  the  concentration  we  obtain  the  molecu- 
lar rise  in  the  boiling-point  of  the  solvent  produced 
by  the  substance  at  the  dilution  in  question.  From  the 
molecular  rise  the  dissociation  is  calculated  very  simply. 
If  there  were  no  dissociation  the  molecular  rise  would 
be  the  boiling-point  constant  of  the  solvent.  If  the 
binary  electrolyte  were  completely  dissociated  the  molecu- 
lar rise  produced  would  be  twice  the  boiling-point  con- 
stant of  the  solvent,  etc. 

If  we  divide  the  molecular  rise  in  question  by  the 
boiling-point  constant^  of  the  solvent  we  obtain  the  van't 
Hoff  coefficient  i. 

If  the  electrolyte  is  binary,  i.  e.,  dissociated  into  two 
ions,  the  dissociation 

a  =  t  —  I 

If  the  electrolyte  is  ternary,  i.  e.,  each  molecule  disso- 
ciated into  three  ions,  the  dissociation 


If  each  molecule  of  the  electrolyte  yields  v  ions,  the 
dissociation 


1  —  I 


To  make  the  above  perfectly  clear  a  few  experimental 
results^  are  given. 

1  This  is  really    the    molecular  rise    of   the  boiling-point  of  a  solvent 
produced  by  a  completely  undissociated,  unpolymerized,  unsolvated  substance. 

2  Jones:  Ztschr.  phys.  Chem.,  31,  129  (1899). 


48  THE   BOIUNG-POINT    METHOD 

Potassium  Bromide  in  Methyi,  Alcohoi,  (C  =  8.4). 


Grams 

Grams 

Concentration 

Rise  in 

Molecular 

Disso- 

CH4O 

KBr. 

molec.  norm. 

B.p. 

rise 

ciation 

56.648 

o.64cx> 

0.00949 

0.119° 

12.54 

49.3 

56.915 

0.7987 

0.01178 

0.149° 

12.65 

50.6 

54.698 

0.8765 

0.01345 

0.170° 

12.64 

50.5 

58.510 

0.8595 

0.01233 

0.156° 

12.65 

50.6 

56.970 

0.9141 

0.01347 

0.170° 

12.62 

50.2 

Potassium  Iodide  in  Ethyi,  Ai^cohoi,  (C  —  11.5) 

. 

Grams 

Grams 

Concentration 

Rise  in 

Molecular 

Disso- 

CaHeO 

KI 

molec.  norm. 

B.p. 

rise 

ciation 

57.084 

0.9035 

0.00954 

0.139° 

1457 

26.7 

55.647 

I.I170 

0.01209 

0.176° 

14.56 

26.6 

55.789 

1.2990 

0.01403 

0.203° 

14.47 

25.8 

58.070 

1.2846 

0.01333 

0.193° 

14.55 

26.5 

58.750 

0.9415 

0.00965 

0.140° 

14.50 

26.1 

PART  III 


THE  CONDUCTIVITY  METHOD 


Conductors  of  electricity  may,  for  the  sake  of  conven- 
ience, be  divided  into  two  classes,  those  that  conduct 
without  undergoing  any  decom|x>sition,  such  as  the 
metals,  carbon,  etc.,  and  those  which,  during  the  passage 
of  the  current,  undergo  a  decomposition  or  electrolysis 
at  the  poles,  such  as  solutions  of  acids,  bases  and  salts.  It 
is  not  at  all  certain  that  there  is  any  fundamental  dif- 
ference between  the  two  classes,  and  at  present,  it  seems 
that  a  very  close  relation  between  the  two  modes  of 
conduction  is  becoming  clearly  recognized. 

It  is  by  no  means  true  that  solutions  of  all  substances 
conduct.  Thus,  aqueous  soultions  of  the  so-called  neu- 
tral organic  compounds,  such  as  the  alcohols,  carbohy- 
drates, urea,  and  a  large  number  of  such  substances,  do 
not  conduct  the  current.  This  furnishes  ground  for  a 
division  of  substances  into  those  whose  solutions  con- 
duct the  current  and  are  called  electrolytes;  and  those 
which,  in  solution,  do  not  conduct  and  are  called  non- 
electrolytes. 

The  application  of  the  conductivity  method  in  phys- 
ical chemistry  is  limited  to  conductors  of  the  so-called 
second  class,  i  e.,  to  solutions  of  electrolytes,  which  are 
chiefly  solutions  of  acids,  bases,  and  salts. 

The  conductivity  of  any  conductor  of  electricity  is  the 
reciprocal  of  its  resistance.  The  resistance  r  is,  from 
Ohm's  law,  expressed  thus: 


r  =■  — r 

t 


50  THE  CONDUCTIVITY   METHOD 

IT  is  the  difference  in  potential  at  the  two  ends  of  the 
conductor,  and  i  is  the  strength  of  the  current.  The  con- 
ductivity c  is  the  reciprocal  of  r. 

i 
c  = —  . 

TT 

The  unit  of  resistance,  called  the  ohm,  is  that  of  a  col- 
umn of  pure  mercury  106.3  cm.  long  and  i  square  mm. 
in  section,  at  0°  C. 

The  Siemens  or  mercury  unit  is  the  resistance  of  a 
column  of  mercury  100  cm.  in  length  and  with  a  cross 
section  of  one  square  mm.  The  two  units  bear  the  rela- 
tion to  another  of  106.3  •  lO^- 

Specific  and  Molecular  Conductivities 

The  resistance  of  conductors  depends  upon  their  form 
as  well  as  upon  their  chemical  nature.  In  order  that 
the  resistances  of  different  conductors  should  be  meas- 
ured in  comparable  quantities,  their  dimensions  must  be 
taken  into  account.  The  dimensions  usually  chosen  are 
a  cylinder  i  meter  in  length  and  i  square  mm.  in  cross 
section.  The  resistance  of  such  forms  of  conductors  is 
known  as  their  specific  resistance.  The  reciprocal  of 
this  is  their  specific  conductivity. 

The  conductors  of  the  so-called  second  class  are  solu- 
tions of  some  electrolyte  in  some  solvent,  and  their  con- 
ductivity depends  chiefly  or  wholly  upon  the  presence 
of  the  electrolytic  substance.  That  the  resistances  of 
such  solutions  should  be  comparable,  it  is  clear  that  we 
must  deal  with  comparable  quantities  of  the  dissolved 
substances.  The  most  convenient  quantities  are  gram- 
molecular  weights. 

Given  a  normal  solution  that  contains  a  gram-molecu- 


the:  conductivity  method  51 

lar  weight  of  the  electrolyte  in  a  liter.  If  this  liter  of 
solution  be  placed  between  two  electrodes  that  are  i 
cm.  apart,  the  cross  section  would  be  1,000  square  centi- 
meters. This  will  have  o.ooi  of  the  resistance,  or  1,000 
times  the  conductivity  of  a  cube  of  the  same  solution 
whose  edge  was  i  cm.  in  length.  If  we  represent  by  v 
the  number  of  cubic  centimeters  of  any  solution  which 
contains  a  gram-molecular  weight  of  the  dissolved  sub- 
stance, and  by  s  the  specific  conductivity  of  a  cube  of 
the  solution  whose  edge  is  i  cm.  in  length,  the  molecu- 
lar conductivity  /*  is  the  product  of  these  quantities : 

\k  •=■  vs. 
But  if  we  represent  by  s  the  specific  conductivity  of  a 
cylinder  of  the  solution  i  meter  in  length  and  i  square 
mm.  in  cross  section: 

fi  =  10,000  vs. 

A  general  expression,  where  g  gram-molecular  weights 
are  contained  in  a  liter  of  the  solution,  is : 

s  X  10' 

when  s,  the  specific  conductivity,  is  referred  to  a  cube 
of  the  solution,  or : 

s  X  10' 

when  s  is  referred  to  a  cylinder  of  the  solution,  one 
meter  in  length  and  a  square  mm,  in  cross  section. 

The  molecular  conductivities  of  solutions  are,  then,  the 
conductivities  of  comparable  quantities  of  different  sub- 
stances, and  when  the  same  dilutions  are  used  the 
molecular  conductivities  are  directly  comparable  with 
one  another. 


52  THE  CONDUCTIVITY  METHOD 

Different  substances  behave  very  differently  with  re- 
spect to  their  power  to  carry  the  current  when  in  solu- 
tion in  a  given  solvent.  The  fundamental  distinction 
between  substances  that  conduct,  and  those  that  do 
not  conduct  at  all,  has  been  already  mentioned.  But 
among  conductors  very  marked  differences  exist.  Some 
reach  a  maximum  of  conductivity  at  moderate  dilution, 
while  others  attain  this  only  at  extreme  dilution. 
Take  the  case  of  a  strong  acid  Hke  hydrochloric  or 
nitric;  the  molecular  conductivity  increases  with  the  di- 
lution to  about  one  one-thousandth  normal,  when  it  be- 
comes constant.  While,  on  the  other  hand,  the  molecu- 
lar conductivity  of  a  weak  acid  like  acetic,  will  increase 
with  the  dilution  as  far  as  the  dilution  can  be  studied 
by  the  conductivity  method. 

The  question  arises,  whence  this  difference  between 
substances  in  respect  to  their  power  to  carry  the  cur- 
rent? Here,  again,  the  theory  of  electrolytic  disso- 
ciation comes  to  our  aid.  Those  substances  that  give 
abnormally  great  depressions  of  the  freezing-point,  ab- 
normally large  elevations  of  the  boiling-point,  and  which 
show  abnormally  great  osmotic  pressures,  conduct  the 
current;  and  only  such  substances  conduct. 

The  explanation  of  the  abnormal  results  with  respect 
to  the  properties  just  mentioned,  was  sought  in  the  dis- 
sociation of  the  molecules  into  ions.  From  a  large 
amount  of  evidence  from  many  sources,  we  seem  justi- 
fied in  concluding  that  only  ions  conduct  the  current. 
Molecules  are  entirely  incapable  of  carrying  electricity 
through  the  solvent  in  which  they  are  dissolved.  If 
only  ions  conduct,  then  the  conductivity  of  a  solution  is 
proportional  to  the   number  of   ions   present,   provided 


the:  conductivity  method  53 

that  the  ions  move  with  the  same  average  velocity,  which 
is  true  of  ions  of  the  same  kind. 

The  conductivity  method  can  then  be  used  to  meas- 
ure the  dissociation  of  electrolytes  in  solution,  and  this 
is  its  most  important  scientific  application.  When  the 
molecular  conductivity  attains  a  maximum  constant 
value,  it  means  that  the  dissociation  is  complete,  and 
this  value  of  the  molecular  conductivity  is  termed  /aoo. 
The  molecular  conductivity  at  any  dilution  is  written  //y. 
in  which  v  is  the  volume  of  the  solution,  i.  e.,  the  number 
of  liters  that  contain  a  gram-molecular  weight  of  the 
electrolyte.  The  percentage  of  dissociation  at  any  dilu- 
tion, a,  is  the  ratio  between  the  molecular  conductivity 
at  that  dilution,  and  the  molecular  conductivity  when 
the  dissociation  is  complete: 


/W,oo 

In  order  to  determine  the  dissociation  of  an  electrolyte 
at  any  given  dilution  by  means  of  the  conductivity 
method,  it  is  necessary  to  determine  the  molecular  con- 
ductivity, \y.v  at  that  dilution,  and  the  value  of  /aoo  for 
the  electrolyte,  when  the  value  of  a  can  be  calculated 
at  once. 

Determination  of  /moo 

The  value  of  /mu  is  determined  directly  for  any  electro- 
lyte in  any  solvent,  by  means  of  the  conductivity 
method.  The  determination  of  /*«>  for  strongly  disso- 
ciated electrolytes  is  comparatively  simple.  The  value 
of  /Au  is  determined  at  a  given  dilution,  the  dilution  in- 
creased, the  molecular  conductivity  determined  at  the 
new  dilution,  and  this  icontinued  until  a  dilution  is 
5 


54 


rut  CONDUCTIVITY  METHOD 


reached  which  is  so  great,  that  when  further  increased 
the  value  of  fiv  remains  the  same.  It  has  then  attained 
a  constant  maximum  value,  which  is  the  value  of  ^loo. 
The  value  of  ftoo  for  strong  acids  and  bases,  and  for 
salts,  is  usually  attained  at  a  dilution  between  v  =  500 
and  V  =  5000.  This  will  be  seen  from  the  following  ex- 
amples : 


Hydrochloric  Acid. 

Potassium  Hydroxide. 

Potassium  Chloride. 

V. 

tJiv  ^8°- 

V. 

flv  18°. 

V. 

flv  ^8°. 

2 

301 

2 

184. 1 

2 

95.8 

32 

335 

20 

204.5 

20 

108.3 

128 

341 

100 

212.4 

100 

1 14. 7 

1000 

346 

500 

214.0 

1000 

1 19-3 

1667 

344 

1000 

211. 1 

5000 

120.9 

A  large  number  of  substances,  such  as  the  organic 
acids  and  bases,  which  are  only  weakly  dissociated  at 
any  ordinary  dilution,  present  a  new  problem  when  it 
is  desired  to  determine  their  maximum  molecular  con- 
ductivity. That  this  is  not  reached  at  dilutions  to 
which  the  conductivity  method  can  be  applied,  is  seen 
from  the  following  examples: 


Acetic  Acid. 

Ammonia 

.1 

V. 

fly  ^8°. 

V. 

f^v  18°. 

2 

1.9 

2 

1.2 

20 

6.2 

20 

4-3 

TOO 

13.2 

100 

9.2 

1000 

38.0 

1000 

26.0 

5000 

79.6 

5000 

50.0 

lOOOO 

99-5 

lOOOO 

61.0 

It  is  evident  from  these  results  that  the  value  of  [xm 
for  such  substances  cannot  be  determined  by  the  method 
given  for  strongly  dissociated  compounds.  The  dilution 
at  which  complete  dissociation  would  take  place  lies  far 
beyond  the  possibility  of  applying  the  conductivity 
method  directly. 

1  Ammonia  is  taken,  since  work  on  the  substituted  ammonias  has  not  gen- 
erally been  carried  to  very  great  dilutions. 


the:  conductivity  method  55 

The  method  of  determining  the  value  of  /too  for  such 
substances  is  as  follows:  While  the  weak  organic  acids 
are  only  slightly  dissociated,  salts  of  these  acids  are 
completely  dissociated  at  moderate  dilutions.  So  also 
with  respect  to  the  weak  bases,  which,  at  ordinary  dilu- 
tions are  only  slightly  dissociated;  their  salts  are  com- 
pletely dissociated  at  dilutions  which  lie  well  within  the 
range  of  the  conductivity  method.  Take  an  organic 
acid.  Its  sodium  salt  is  prepared  and  the  value  of  fioo 
for  this  salt  is  determined ;  or  taking  an  organic  base,  the 
nitrate  of  the  base  is  used  and  the  value  of  /a^  for  the 
nitrate  determined. 

It  remains  to  see  what  relation  exists  between  the 
value  of  /xoo  for  the  sodium  salt  of  an  acid  and  the  acid 
itself,  or  between  the  nitrate  of  a  base  and  the  base. 

Kohlrausch*  has  shown  that  the  value  of  fi^  for  any 
compound  is  the  sum  of  two  constants,  the  one  depend- 
ing upon  the  cation,  the  other  upon  the  anion.  The 
value  of  fxoo  for  sodium  acetate  is  the  sum  of  two  con- 
stants, the  one  for  the  cation,  sodium,  and  the  other  for 
the  anion,  CH3COO.  If  the  constant  for  sodium  be 
subtracted,  the  remainder  is  the  constant  for  the  anion 
of  acetic  acid.  If  to  this  constant  the  constant  for  hy- 
drogen be  added,  we  have  the  value  of  /*«  for  acetic 
acid  itself.  Exactly  the  same  line  of  reasoning  applies 
to  the  nitrate  of  the  base. 

The  constant  for  NO3  is  substracted  from  ft*  for  the 
nitrate,  and  the  remainder  is  the  constant  for  the  cation 
of  the  base.  To  this  the  constant  for  hydroxyl  is  added, 
and  the  sum  is  the  value  of  /a»  for  the  base. 

The  value  of  the  constant  for  sodium  is  49.2  at  25°, 
and  of  hydrogen,  325  at  25°.     If  we  add  275.8  to  the 

1  Wied.  Ann.,  6,  167  (1879). 


56  the:  conductivity  method 

value  of  /Moo  for  the  sodium  salt  of  an  acid,  we  have  the 
value  af  />t»  for  the  acid.  The  value  of  the  constant  for 
NO3,  at  the  same  temperature,  is  65.1,  and  for  (OH), 
170.  We  must,  therefore,  add  105  to  /*«  for  the  nitrate 
of  a  base,  in  order  to  ascertain  /xoo  for  the  base  itself. 

It  is  thus  possible  to  determine  fxoo  for  compounds 
that  are  only  slightly  dissociated  at  ordinary  dilutions. 
Since  /x»  can  always  be  determined  for  any  electrolyte, 
we  are  able  to  measure  the  dissociation  of  compounds, 
which,  even  in  water,  are  only  slightly  dissociated. 

The  application  of  the  conductivity  method  to  meas- 
ure the  exact  dissociation  in  solvents  other  than  water 
is  not  usually  successful.  Water  exercises  the  strong- 
est dissociating  action  of  any  known  solvent.  The  ion- 
izing power  of  many  solvents  is  so  weak,  that  it  is  impos- 
sible to  determine  the  value  of  /xoo  for  electrolytes  dis- 
solved in  them  by  the  direct  application  of  the  con- 
ductivity method.  In  such  cases,  it  is  possible  to  deter- 
mine the  dissociation  only  approximately. 

The  general  applicability  of  any  method  of  measuring 
electrolytic  dissociation  is  of  wide-reaching  significance. 
This  will  appear,  when  we  consider  that  most  chemical 
reactions  take  place  between  ions,  molecules  as  such  not 
coming  into  play.  The  chemical  activity  of  solutions  is 
then  a  function  of  the  dissociation,  and  since  conduc- 
tivity is  a  measure  of  dissociation,  there  is  a  close  rela- 
tion between  the  conductivity  of  solutions,  and  their 
power  to  react  chemically.  Indeed,  the  former  has  often 
been  used  to  measure  the  latter. 

In  this  connection  is  to  be  mentioned,  especially,  the 
work  of  Ostwald^  on  the  conductivity  of  organic  acids, 
from  which  he   calculated  their  dissociation  constants. 

*  Ztschr.  phys.  Chem.,  3,  170,  241,  369  (1889). 


THE  CONDUCTIVITY   METHOD  57 

Knowing  the  dissociation  constant,  the  chemical  activity 
of  the  acid  is  known.  The  work  of  Bredig^  on  the  con- 
ductivity of  organic  bases  is  strictly  analogous  to  that 
just  cited, 

Ostwald^  has  also  shown  that  it  is  possible  to  deter- 
mine the  basicity  of  acids  by  determining  the  conduc- 
tivities of  their  sodium  salts. 

The  conductivity  method  has  also  been  extensively 
applied  to  determine  what  we  have  already  called  the 
constants  for  the  ions,  or  the  relative  velocities  with 
which  the  ions  move  through  the  solutions. 

A  large  number  of  applications  of  the  conductivity 
method  to  special  problems  in  dissociation  have  been 
made  in  the  last  few  years,  so  that  it  may  be  said  to  be 
one  of  the  most  important  of  all  the  physical  chemical 
methods. 

The  Application  of  the  Conductivity  Method   to   the 
Measurement  of  Electrolytic  Dissociation 

When  a  continuous  current  is  passed  through  a  solu- 
tion of  an  electrolyte  the  electrodes  become  quickly 
covered  with  gas,  or,  as  we  say,  become  polarized.  This 
increases  the  resistance  to  the  passage  of  the  current,  and 
interferes  with  the  measurement  of  the  resistance  of  the 
solution.  Several  devices  have  been  proposed  for  over- 
coming the  effect  of  polarization,^  but  none  has  proved 
as  simple  as  the  use  of  the  alternating  current.  The 
effect  of  polarization,  tending  to  retard  the  flow  of  the 
current  in  one  direction,  is  practically  counterbalanced  by 
the  action  in  the  opposite  direction,  where  the  polarization 

1  Ibid,  13,  289   (1894). 

2  Ztschr.  phys.  Cheni  ,  1,  105  (1887);  2,  902  (1888). 

3  Stroud  aud  Henderson  :  Phil.  Mag.,  43,  19  (1897). 


58  the;  conductivity  method 

current  adds  itself  to  the  original.  This  method  of 
measuring  the  conductivity  of  solutions  we  owe  to  Kohl- 
rausch. 

The  apparatus  employed  is  sketched  diagrammatically 
in  Fig.  9.  J  is  a  small  induction  coil,  with  only  one  or 
two  layers  of  wire.  A  larger  coil  must  not  be  used, 
since  it  does  not  give  a  sharp  tone  minimum  in  the  tele- 
phone. The  coil,  tuned  to  a  very  high  pitch,  should  be 
inclosed  in  a  box  surrounded  by  a  poor  conductor  of 


sound,  and  placed  at  some  distance  from  the  bridge 
where  the  reading  is  to  be  made.  The  coil  is  driven  by  a 
storage  cell  of  medium  size.  A  platinum  wire,  or  bet- 
ter one  of  manganese  alloy  which  has  a  small  tempera- 
ture coefficient  of  resistance,  is  tightly  stretched  over  the 
meter  stick  AB  which  is  carefully  divided  into  millime- 
ters. A  rheostat  W,  whose  total  resistance  amounts  to 
11,110  ohms,  is  convenient.  The  resistance  vessel  R, 
containing  the  solution  and  electrodes,  is  shown  enlarged 
in  Fig.  10.  The  electrodes  are  cut  from  thick  sheet 
platinum,  and  into  each  plate  a  stout  platinum  wire, 
about  an  inch  in  length,  is  welded.  Glass  tubes  are 
sealed  on  to  the  platinum  wires  and  electrode  plates,  by 
means  of  sealing  glass,  as  shown  in  the  drawing.  These 


the;  conductivity  method 


59 


tubes  pass  tightly  through  a  ground-glass  stopper,  which 
fits  into  the  glass  vessel.  They  are  filled  to  a  convenient 
height  with  mercury,  and  electrical  connection  established 
by  means  of  copper  wires,  which  dip  into  the  mercury. 
One  arm  of  the  telephone  T  is  thrown  into  the  circuit 


Fig.  10, 

between  the  rheostat  and  the  resistance,  and  the  other 
arm  is  connected  with  the  bridge  wire,  by  means  of  a 
slider.  This  is  moved  along  the  wire  until  that  point 
is  found  at  which  the  hum  of  the  induction  coil  ceases  to 
be  heard  in  the  telephone.    Let  this  be  some  point  c,  and 


60  rut  CONDUCTIVITY  METHOD 

let  us  represent  Ac  by  a,  and  Be  by  b,  the  resistance  of 
the  solution  in  the  vessel  R  by  r,  and  the  resistance  in 
ohms  in  the  rheostat  by  w;  then,  from  the  principle  of 
the  bridge,  we  have: 

ra  =■  wb. 

wb 

a 

But  the  conductivity  of  a  solution  c  is  the  reciprocal  of 
the  resistance  r;  therefore, 

a 

wb 
The  conductivity  of  solutions,  determined  by  this  ex- 
pression, would  not,  in  any  sense,  be  comparable  with 
one  another,  since  there  is  nothing  in  the  expression 
that  takes  into  account  the  concentration  of  the  solu- 
tion. It  is  most  convenient  to  refer  all  concentrations 
to  gram-molecular  normal,  containing  a  gram-molecular 
weight  of  the  electrolyte  in  a  liter.  If  we  represent  by 
V  the  number  of  liters  that  contain  a  gram-molecular 
weight  of  the  dissolved  substance,  the  preceding  expres- 
sion becomes — 

va 

wb 
Instead  of  the  conductivity  c,  we  write  for  the  molecu- 
lar  conductivity,   /x,   and  to   indicate   the   concentration 
at  which  the  /a  is  determined,   we  write  /a-,,,  in  which  v 
has  the  significance  indicated  above. 

va 


wb 

But  even  this  expression  does  not  take  into  account  the 
dimensions  of  the  cell  used.    A  cell-constant  C  must  be 


TH^  CONDUCTIVITY   METHOD 


6i 


introduced  and  determined  for  each  cell,  before  the  cell 
can  be  employed  for  conductivity  measurements.  The 
complete  expression  for  the  molecular  conductivity  is 
then — 


fJi-v  =  C 


Va 


wb 


Wheatstone  Bridge 

Instead  of  the  straight  wire  bridge  sketched  diagram- 
matically  in  figure  9,  it  is  far  better  to  use  the  form  indi- 
This   form  is  furnished  by  Leeds 


cated  in  figure 


II. 


Fig.  II. 

and  Northrup,  of  Philadelphia,  from  whose  catalogue  the 
above  sketch  was  taken. 

The  manganine  wire  is  wrapped  around  a  marble  cyl- 
inder which  is  about  15  cm.  in  diameter.    Instead  of  one 


62  the:  conductivity  method 

meter  a  wire  about  five  meters  in  length  is  used,  and  thus 
the  error  in  reading  is  reduced  about  five  times.  This 
form  of  bridge  occupies  much  less  space  than  the  straight 
form,  is  much  more  convenient  to  handle,  and,  as  stated, 
is  far  more  accurate. 

Temperature  Coefficient  of  Conductivity 

The  conductivity  of  solutions  of  electrolytes  increases 
rapidly  with  rise  in  temperature.  The  molecular  conduc- 
tivity of  a  quarter-normal  solution  of  hydrochloric  acid, 
which  is  223.3  a-t  10°,  rises  to  397.9  at  35°.  This  is  even 
more  marked  in  the  case  of  sodium  sulphate;  a  quarter- 
normal  solution  having  a  conductivity  of  68.5,  at  0°  has 
a  conductivity  of  156.1  at  35°. 

From  this  it  is  evident,  that  a  definite,  constant  tem- 
perature must  be  carefully  maintained  in  all  conductivity 
work.  This  is  accomplished  by  placing  the  vessel  con- 
taining the  solution  in  a  large  volume  of  water  which  is 
maintained  at  a  constant,  known  temperature.  A  con- 
venient form  of  thermostat  (Fig.  12)  for  such  work  is 
used  in  the  laboratory.  A  double-walled  metallic  vessel, 
holding  from  15  to  20  liters  of  water,  is  stirred  by  pad- 
dles driven  by  a  hot-air  motor,  which  is  kept  in  motion  by 
means  of  a  small  gas  jet  placed  beneath  it.  The  space  be- 
tween the  two  walls  is  filled  with  asbestos  cement.  A  large 
glass  tube  placed  near  the  bottom  of  the  vessel  is  filled 
with  a  10  per  cent,  solution  of  calcium  chloride.  The 
change  in  volume  of  this  solution  with  temperature,  can  be 
used  to  regulate  the  temperature  of  the  water-bath. 

The  Ostwald  regulator  (Fig.  13)  can  be  easily  ad- 
justed, so  that  the  temperature  of  the  water-bath  will  re- 
main constant  to  within  one-tenth  of  a  degree  for  a  day. 


TH]^  CONDUCTIVITY   ME:TH0D 


63 


Tube  A  is  connected  with  the  gas  supply.  The  glass 
tube  C,  which  opens  just  above  the  mercury  meniscus, 
contains  a  'fine  perforation  in  the  side,  so  as  to  supply 


Fig.  12. 


gas  enough  to  keep  the  flame  alive,  when  the  lower  end 
of  the  tube  is  closed  by  the  mercury.  Tube  B  connects 
with  the  burner,  and  D  with  the  large  tube  containing  the 


64 


THE  CONDUCTIVITY   METHOD 


calcium  chloride  solution,  resting  on  the  bottom  of  the 
water-bath. 


Pig.  13. 

When  it  is  desired  to  adjust  the  regulator  for  a  defi- 
nite temperature,  the  stop-cock  is  opened,  the  flame 
lighted,  and  a  thermometer  divided  into  tenths  of  a  de- 
gree, suspended  in  the  bath.  The  end  of  tube  C  is 
raised  above  the  mercury  surface,  and  the  stirrer  is  set 
in  motion  by  means  of  the  hot-air  motor.  When  the 
thermometer  registers  the  desired  temperature  the  stop- 
cock is  closed,  and  the  end  of  tube  C  is  pushed  down 
until  it  just  touches  the  mercury  surface.  The  apparatus 
will  then  control  the  temperature  automatically.  A  very 
efficient  electrically  controlled  regulator  has  recently 
been  described  by  Reid,^  and  a  part  of  this  is  shown  in 
Fig.  12. 

A  very  convenient  temperature  to  use  for  routine  work 
with  the  conductivity  method  is  zero  degrees.  Fur- 
thermore, this  is  an  easy  temperature  to  realize  and  to 
maintain. 

Take  a  battery  jar  and  fill  it  with  finely  crushed 
ice.     Then  add  just  enough  distilled  water  to  moisten 

1  Amer.  Chem.  Journ.,  41,  148  (1909). 


the;  conductivity  method  65 

the  ice.    If  more  water  is  added  the  temperature  always 
remains  somewhat  above  zero. 

Place  the,  battery  jar  in  question  in  a  larger  vessel 
and  fill  the  space  between  the  two  vessels  with  ice  and 
water.  Place  the  conductivity  cell  containing  the  solu- 
tion in  the  innermost  vessel,  and  within  an  hour  or  so  the 
solution  if  stirred  will  be  within  a  few  hundredths  of  a 
degree  of  zero. 

Calibrating  the  Wire 

A  stout  platinum  wire  can  be  used  in  constructing  the 
Wheatstone  bridge,  but,  as  already  stated,  it  is  better 
to  use  one  of  an  alloy  of  manganese  (manganine).  This 
wire  is  usually  of  very  nearly  uniform  resistance,  but 
this  can  never  be  taken  for  granted  without  testing  it. 
A  convenient  method  for  calibrating  such  a  wire  has 
been  described  by  Strouhal  and  Barus.^  A  piece  of 
German-silver  wire  about  a  meter  and  a  half  in  length, 
is  cut  into  ten  pieces  (Fig.  14),  which  are,  as  nearly  as 


Fig.  14. 

possible,  of  the  same  length.  The  insulation  is  removed 
from  the  ends  of  these  wires,  and  they  are  soldered  on  to 
thick  copper  wires  about  an  inch  in  length.  Nine  holes 
are  made  in  a  board,  which  is  about  a  meter  in  length, 
at  equal  distances  apart.  These  are  partly  filled  with 
mercury,  and  receive  the  ends  of  the  copper  wires  which 

1  Wied.  Ann.,  lo,  326  (1880). 


66  THE  CONDUCTIVITY   METHOD 

have  been  previously  amalgamated.  The  board,  with 
wires  in  position,  is  placed  along  by  the  side  of  the 
bridge  wire,  and  the  two  end  loops  attached  to  the  ex- 
tremities of  the  bridge.  The  current  from  the  small  in- 
ductorium  is  passed  through  the  bridge,  and  also 
through  the  series  of  loops.  One  of  the  loops  is  chosen 
as  the  standard  and  is  suitably  marked  so  as  to  dis- 
tinguish it  from  the  others.  One  end  of  this  standard 
is  attached  to  one  end  of  the  bridge,  and  the  other 
placed  in  the  first  mercury  cup.  One  arm  of  the  tele- 
phone  is  placed  in  the  same  mercury  cup,  and  the  other 
attached  to  the  pointer,  which  moves  along  the  bridge 
wire.  The  point  of  silence  on  the  bridge  is  ascertained. 
This  is  the  first  reading  for  point  i.  The  telephone, 
and  all  other  connections  remaining  unchanged,  the  stand- 
ard measuring  wire  which  was  at  position  i,  is  moved  to 
position  2,  and  wire  2  is  placed  in  position  i.  A  reading 
is  again  made  in  the  telephone  which  is  the  second 
reading  for  position  i.  The  arm  of  the  telephone, 
which  was  in  cup  i,  is  then  removed  to  cup  2,  and 
the  point  of  silence  ascertained.  This  is  the  first  reading 
for  cup  2.  The  standard  wire  which  is  now  in  position 
2,  is  moved  to  position  3,  wire  3  is  taken  back  to  2, 
and  all  other  connections  are  unchanged.  The  point 
of  equilibrium  is  again  ascertained  at  2,  which  gives  the 
second  reading  for  this  position.  The  standard  wire 
is  thus  interchanged  in  position  with  each  of  the  loops, 
and  two  readings  obtained  on  the  bridge  for  each  position 
except  the  last,  for  which  only  one  reading  is  available. 

It  must  be  observed  that  in  all  such  work  in  which  the 
telephone  is  used  it  is  not  advisable  to  try  to  ascertain 
directly  the  exact  point  on  the  wire  at  which  the  coil 


the:  conductivity   ME:TH0D  (i'J 

cannot  be  heard,  or  at  which  the  tone  is  a  minimum; 
but  to  find  a  point  on  each  side  of  the  true  zero,  at 
which  the  intensity  of  the  tone  is  the  same.  These  two 
readings  should,  at  most,  be  not  more  than  a  centimeter 
apart.  The  true  zero  is  then  just  half-way  between 
these  points. 

The  bridge  wire  is  thus  divided  into  ten  lengths.  The 
application  of  the  calibration  correction  is  simple.  The 
ten  values  are  added  together,  and  their  sum  subtracted 
from  I, GOO  mm.  The  difference  is  divided  into  lo  parts 
and  each  length  is  corrected  by  this  amount,  so  that  the 
sum  is  I, GOO  mm.  By  adding  the  parts  thus,  i,  1+2, 
etc.,  we  obtain  the  points  which  correspond  to  tenths  of 
the  wire.  The  difference  between  these  and  10,  20,  etc., 
gives  the  correction  to  be  applied. 

Carrying  Out  a  Conductivity  Measurement 

After  the  wire  is  calibrated,  the  next  step  is  to  deter- 
m.ine  the  value  of  the  constant  (C)  for  the  cell  which  is 
to  be  used.  The  preparation  of  the  cell  is  a  matter  of 
some  care.  In  the  first  place,  the  electrodes  must  be 
placed  at  a  convenient  distance  apart,  by  shoving  the 
glass  tubes  through  the  stopper,  and  these  must  then 
be  fastened  firmly  in  the  stopper,  so  that  no  further 
movement  is  possible.  If  a  fairly  concentrated  solution 
is  to  be  studied,  the  plates  must  be  as  much  as  2,  or  3 
cm.  apart.  If  a  very  dilute  solution  is  to  be  used,  a 
distance  of  0.5  cm.  is  sufficient.  The  ordinary  white 
platinum  plates,  such  as  are  furnished  by  the  manu- 
facturers, cannot  be  used  directly  since  they  would  not 
give  a  sharp  tone-minimum  in  the  telephone.  They 
must  be  carefully  cleansed  by  washing  in  chromic  acid, 


68  the:  conductivity  me:thod 

and  then  in  water.  A  few  drops  of  a  solution  of  pla- 
tinic  chloride  are  poured  into  the  conductivity  cell,  (Fig. 
lo)  and  the  cell  filled  with  pure  water  until  the  elec- 
trodes are  covered.  A  current  from  a  storage  battery  is 
then  passed  through  the  solution  until  the  electrodes 
become  more  and  more  deeply  blackened.  The  direction 
of  the  current  should  be  frequently  reversed,  so  that  both 
electrodes  may  become  coated,  and  in  order  that  the  de- 
posit may  be  as  nearly  uniform  as  possible.  After  the 
plates  are  completely  covered  with  a  layer  of  platinum 
black,  the  platinic  chloride  is  removed  from  the  cell,  a 
little  sodium  hydroxide  added  and  the  current  is  passed 
through  this  solution.  The  object  of  the  alkali  is  to 
remove  any  chlorine  which  may  have  been  retained  by 
the  platinum  black  as  it  was  being  deposited.  The  sodium 
hydroxide  is  then  removed  by  hydrochloric  acid,  and  the 
acid  by  repeated  washing  with  pure  redistilled  water. 
In  order  to  determine  the  value  of  C,  in  the  expression, 

for  any  cell,  it  is  necessary  to  use  some  solution  for 
which  the  value  fiv  is  known.  Since  potassium  chlo- 
ride can  generally  be  obtained  in  a  high  degree  of  purity, 
by  five  or  six  crystallizations,  it  is  convenient  to  use 
in  standardizing  the  cell.  A  one-fiftieth  normal  solution 
of  potassium  chloride  has  a  molecular  conductivity  (/au) 
of  129.7  at  25°  C.  and  70.8  at  0°.  The  solution  is  poured 
into  the  cell  until  the  electrodes  are  covered,  and  brought 
to  exactly  25°  C.  or  0°  in  the  thermostat.  The  bubbles  of 
ail  which  usually  separate  on  the  electrodes  with  rise  in 
temperature,  having  been  removed,  a  resistance  is  thrown 
into  the  circuit  by  means  of  the  rheostat,  which  will 


TH^  CONDUCTIVITY   METHOD  69 

bring  the  point  of  tone-minimum  not  very  distant  from 
the  center  of  the  bridge.  Thus,  all  the  quantities  in  the 
above  expression  except  C,  are  known,  and  the  equation 
can  therefore  be  solved  at  once  for  the  value  of  C. 

The  constant  for  any  given  cell  being  determined,  it  is 
a  matter  of  fundamental  importance  that  its  value  should 
not  be  changed.  This  would  be  done  if  the  electrodes 
were  moved  with  respect  to  one  another,  or  their  sur- 
faces in  any  wise  altered.  It  is  therefore  necessary 
that  the  electrodes  should  never  be  placed  upon  a  hard 
surface,  but  always  upon  clean,  thick,  filter-paper,  and  the 
plates  must  never  be  touched  with  any  hard  object. 

Knowing  the  constant  for  the  cell,  the  measurement 
of  the  conductivity  of  a  solution  involves  exactly  the 
same  procedure  as  that  just  described.  The  difference 
is  in  the  calculation.  C  is  known  and  it  is  desired  to 
find  the  value  of  /a^  for  a  given  solution. 

The  solution  is  placed  in  the  cell,  brought  to  25°  C.  or 
0°,  the  resistance  introduced  in  the  rheostat  and  the  bal- 
ance effected  on  the  bridge.  All  the  values  in  the  above 
expression  are  known  except  n-v,  which  is  calculated 
directly. 

If  the  solution  used  is  more  concentrated  than  2^^^ 
normal,  it  is  better  to  use  the  cell  with  electrodes  far 
apart.  If  more  dilute,  the  electrodes  whose  distance 
from  one  another  is  not  more  than  0.5  cm.  should  be 
employed. 

Precautions  are  necessary  at  every  turn.  The  wire 
after  calibration,  must  never  be  touched  with  the  hand 
on  account  of  grease,  and  the  point  of  contact  with  the 
wire  must  be  moved  over  its  surface  very  carefully.  The 
current  must  not  be  allowed  to  flow  through  the  resist- 
7 


70  THE  CONDUCTIVITY   MEiTHOD 

ance  coils  for  any  considerable  length  of  time,  or  the  tem- 
perature, and  therefore  the  resistance  of  the  coils  will 
change.  The  inductorium  should  be  allowed  to  run  only 
during  the  actual  measurement  of  the  resistance.  Es- 
pecial care  should  be  taken  that  every  connection  is  clean 
and  well  made,  otherwise  resistance  will  be  introduced  at 
the  junctions. 

Correction  for  the  Conductivity  of  Water 

Since  water  is  the  most  general  solvent  known,  and 
solutions  in  this  solvent  have  the  greatest  conductivity, 
one  is  called  upon  most  frequently  to  measure  the  conduc- 
tivity of  aqueous  solutions.  In  all  such  cases  the  quan- 
tity actually  measured  is  the  sum  of  the  conductivities 
of  the  water  and  of  the  dissolved  electrolyte.  The  con- 
ductivity of  the  vv-ater  alone,  must,  in  every  case,  be  de- 
termined, in  order  that  the  conducting  power  of  the 
electrolyte  may  be  ascertained.  It  would,  at  first  sight, 
appear  to  be  possible  to  use  water  of  only  a  fair  degree 
of  purity,  to  determine  its  conductivity,  and  then  to  sub- 
tract this  from  the  conductivity  of  the  solution.  Whether 
this  could  be  done,  would  depend  upon  the  nature  of 
the  impurities. 

They  might  easily  be  of  such  a  character  as  to  react 
chemically  with  the  dissolved  electrolyte,  and  thus  seri- 
ously affect  the  nature  of  the  solution.  Thus,  ammonia, 
which  would  neutralize  any  acid  forming  a  salt,  would 
materially  change  the  nature  of  the  ions  present,  and 
therefore  the  conductivity.  Carbon  dioxide  would,  in 
like  manner,  afifect  the  conductivity  of  any  strong  base. 
It  is  therefore  necessary,  in  all  work  involving  the  use  of 
the  conductivity  method,  to  prepare  water  in  as  pure  con- 


the;  conductivity  method  71 

dition  as  is  practicable,  and  then  to  introduce  a  correc- 
tion for  its  conductivity  when  this  is  larger  than  the 
necessary  experimental  error. 

Kohlrausch^  has  prepared  the  purest  water  thus  far 
obtained,  by  distilling  the  purest  water  obtainable  by 
other  methods  in  a  vacuum.  He  determined  its  con- 
ductivity without  exposure  to  the  air,  and  found  it  to  be 
0.04  X  lO"*'.  To  prepare  water  of  this  degree  of  purity 
is  not  practicable,  and  indeed  is  not  necessary  for  con- 
ductivity work. 

Nernst^  has  suggested  fractional  crystallization  as  a 
means  of  purifying  water  for  conductivity  purposes,  but 
equally  efficient  and  far  more  rapid  methods  have  been 
subsequently  devised. 

Hulett^  has  obtained  water  of  a  high  degree  of  purity, 
by  distilling  it  first  from  potassium  bichromate  and  sul- 
phuric acid,  and  then  redistilling  from  a  solution  of 
barium  hydroxide.  The  water  purified  in  this  way  had 
a  conductivity  of  from  07  to  0.8  X  io~**. 

More  recently,  Jones  and  Mackay*  have  used  an  appa- 
ratus in  which  the  water  is  distilled  first  from  acid  potas- 
sium bichromate,  which  decomposes  any  organic  matter 
present  and  retains  the  ammonia,  and  second  from 
barium  hydroxide  which  retains  any  carbon  dioxide. 
The  apparatus  is  shown  in  Fig.  15.  Ordinary 
distilled  water  with  a  little  sulphuric  acid  and  potassium 
bichromate,  are  distilled  from  a  Jena  glass  balloon  flask 
and  condensed  in  a  tube  of  block  tin.  It  is  then  boiled 
in  A  from  barium  hydroxide,  the  vapor  passing  into  B, 
which  contains  distilled  water,  and  a  little  barium  hydrox- 

1  Ztschr.  phys.  Chetn.,  14,  317  (1894). 

^  Ibid,  8,  120  (1891). 

^  Ibid,  ai,  297(1896), 

<  Araer.  Chem.  Journ.,  19,  91  (1897);  Ztschr.  phys.  Cheni.,  23,  237  (i?97). 


72 


THE  CONDUCTIVITY   ME^THOD 


ide.  A  small  flame  is  sufficient  to  keep  the  liquid  in  B  at 
the  boiling  temperature.  The  vapor  passes  from  B  along 
the  long  neck  of  the  retort,  into  the  tin  condenser,  and 
is  received  in  the  flask  E.  Certain  precautions  must  be 
taken  in  fitting  up  and  using  the  apparatus.  Vessels  A 
and  B  are  connected  with  a  tube  of  block  tin  H.  When- 
ever the  apparatus  is  cleaned  and  refilled,  which  should  be 
done  about  once  a  month  when  in  constant  use,  the  dis- 
tillate collected  at  first  must  be  discarded.  The  carbon 
dioxide  not  absorbed  in  A,  is  absorbed  by  the  alkali  in  B. 


Fig.  15. 

The  process  is  thus  perfectly  continuous  for  a  least  a 
month,  or  it  can  be  interrupted  at  any  time  by  removing 
the  burner.  Eight  to  ten  liters  of  water  can  be  obtained 
daily  with  the  use  of  this  apparatus. 

The  water  purified  by  this  method  gave  a  conductivity 
at  25°,  varying  from  i  to  1.5  X  io~^  in  mercury  units. 

The  correction  which  must  be  applied  to  the  values  of 
fiv,  for  the  conductivity  of  the  water  employed  in  pre- 
paring the   solutions,   is  calculated  by  multiplying  the 


specific   conductivity  of  the  water 


w5 


by  the  volume 


of  the  solution  in  liters.    This  quantity  for  water  properly 


THE  CONDUCTIVITY   ME;TH0D  73 

purified,  is  negligible  for  concentrated  solutions,  and 
attains  an  appreciable  value  only  in  dilute  solutions.  In 
case  the  'substance  under  investigation  reacts  chemically 
with  the  impurities  in  the  water,  such  a  correction  would 
be  so  uncertain  that  it  is  better  not  to  attempt  to  apply 
it  except  at  very  high  dilutions. 

Substances  to  be  Used 

In  practice",  it  is  well  to  use  some  of  the  same  sub- 
stances whose  freezing-point  lowerings  have  been  meas- 
ured, so  that  the  dissociation  as  determined  by  conductiv- 
ity may  be  compared  with  that  calculated  from  the  de- 
pression of  the  freezing-point.  Prepare  say,  a  tenth-, 
normal  solution  of  the  substance  chosen,  determine  the 
value  of  ft^  for  this  dilution,  increase  the  dilution  to  i^^-, 
sUf  ttjVt7>  and  -^^Vo-*  normal,  determining  in  each  case 
the  value  of  /jl^.  At  about  TTAyiF>  f^v  will  become  con- 
stant for  most  of  the  strong  binary  electrolytes, 
and  will  show  no  further  increase  with  increase  in  the 
dilution.  This  is  the  value  of  fioo.  To  find  the  per- 
centage of  dissociation,  a,  at  any  dilution,  divide  the 
value  of  /x^  at  that  dilution  by  the  value  of  /w-oo  for  the 
substance  in  question. 

a  = . 

floo 

Results  for  a  Few  Substances 

Some  results  for  the  conductivity  and  dissociation  of 
a  few  typical  electrolytes  will  give  an  idea  of  the  order 
of  magnitude  of  these  values,  and  the  way  in  which 
they  change  with  temperature  and  dilution.  The  molecu- 
lar conductivities  are  represented  by  /u,^,  the  dissociation 
by  a  and  the  volume  of  the  solution  by  v. 


74  THK  CONDUCTIVITY   MliTHOD 


Hydrocht.oric  Acid.* 

xoo  /A7/25°  a250  /X^35°  a  35^ 


4 

223.3 

93-5 

348.2 

91.8 

397.9 

91.8 

8 

227.0 

95.1 

357.0 

94.1 

407.1 

93.9 

i6 

231-8 

97.1 

365.2 

96-3 

415.5 

95.9 

32 

235.0 

98.4 

370.7 

97-7 

423.4 

97.7 

128 

238.8 

lOO.O 

379-3 

lOO.O 

433-3 

lOO.O 

Sui^PHURic  Acid.' 

V. 

/^.o° 

aoo 

/Az.25° 

aaso 

/A.  35° 

a  35° 

4 

292.9 

65.2 

419.3 

59.1 

457.2 

56.1 

8 

303.9 

67.7 

431.5 

60.8 

471-7 

57.9 

i6 

323.6 

72.0 

456.6 

64.3 

498.0 

61.2 

32 

347.2 

77.3 

491.4 

69.2 

533.6 

65.5 

128 

403.6 

89.8 

589-4 

83.0 

646.2 

79-3 

512 

442.7 

98.6 

675.2 

95.1 

753.0 

92.5 

2048 

449.2 

lOO.O 

709.9 

lOO.O 

814.4 

lOO.O 

Potassium  Chi^oridk.' 

I/. 

1^.0- 

aoo 

A*^25° 

a  25° 

/A^50° 

a  50° 

2 

62.96 

83.8 

109.5 

79.9 

161. 9 

76.3 

8 

66.47 

88.5 

II8.6 

86.6 

179.I 

84.4 

32 

68.40 

93.5 

122.9 

92.6 

192.8 

90.9 

128 

70.27 

97.2 

126.8 

96.6 

204.3 

96.3 

512 

73.00 

98.8 

132.4 

98.9 

209.1 

98.6 

1024 

74-24 

lOO.O 

135.5 

lOO.O 

211. 6 

99.8 

2048 

75.14 

137.0 

212. 1 

loo.o 

Potassium  SuIvPhate.* 

V. 

/^.o° 

aoo 

l^.,  25° 

a  25° 

/A^50° 

2 

87.19 

60.1 

152.6 

56-9 

224.8 

8 

101.9 

70.3 

183.6 

68.5 

276.7 

32 

117.9 

81.3 

214.4 

80.0 

329.2 

128 

131.9 

91.0 

242.1 

90.3 

376.0 

512 

142.7 

98.4 

263.5 

98.3 

406.7 

1024 

145.0 

lOO.O 

268.0 

lOO.O 

419.6 

1  Jones  and  West:  Amer.  Chem.  Journ.,  34,  412  (1905). 
«  Jones  and  West:  Ibid  34,  415  (1905). 

3  Jones  and  West:  Ibid.,  34,  381   (1905);  Jones  and  Clover,  Ibid.,  43,  202 
(1910). 

<  Jones  and  West:  Ibid,  34,  387  (1905). 
6  Jones  and  Clover:  43,  203  (1910). 


THE  CONDUCTIVITY   METHOD  75 

The  conductivity  of  sulphuric  acid  is  greater  than  that 
of  hydrochloric,  since  the  molecule  of  hydrochloric  acid 
dissociates  into  two  ions,  while  the  molecule  of  sulphuric 
acid  dissociates  into  three.  The  same  applies  to  potas- 
sium chloride  as  compared  with  potassium  sulphate. 

The  conductivity  of  a  strong  acid  is  greater  than  that 
of  its  salts,  because  the  hydrogen  ion  has  a  much  greater 
velocity  than  that  of  any  other  cation.  It  should  be 
noted  that  the  dissociation  decreases  slightly  with  rise 
in  temperature.  This  is  a  general  phenomenon  among 
electrolytes. 

The  dissociation  increases  with  the  dilution  until  com- 
plete dissociation  is  reached. 


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